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International Library of Psychology 
Philosophy and Scientific Method 


Chance, Love and Logic 







International Library of Psychology 
Philosophy and Scientific Method 

General Editor: C. K. Ogden, m.a 

VOLUMES ALREADY PUBLISHED 

'PHILOSOPHICAL STUDIES, by G. E. Moore, Litt.D. 

* THE MISUSE OF MIND, by Karin Stephen. Prefatory note 

by Henri Bergson 

'CONFLICT AND DREAM, by W. H. R. Risers, F.R.S. 
'PSYCHOLOGY AND POLITICS, by W. H. R. Rivers, F.R.S. 
‘TRACTATUS LOGICO-PHILOSOPHICUS, by L. Wittgenstein. 
Introduction by Bertrand Russell 

THE MEASUREMENT OF EMOTION, by W. Whately Smith. 

Introduction by William Brown 
‘PSYCHOLOGICAL TYPES, by C. G. Jung, M.D., LL.D. 
SCIENTIFIC THOUGHT, by C. D. Broad, Litt.D. 

-THE MEANING OF MEANING, by C. K. Ogden and I. A. 
Richards 

CHARACTER AND THE UNCONSCIOUS, by J. H. van der 
Hoop 

IN PREPARATION 

* SCIENTIFIC METHOD, by A. D. Ritchie 

THE ANALYSIS OF MATTER, by Bertrand Russell, F.R.S. 
TSYCHOLOGY AND ETHNOLOGY, by W. H. R. Rivers, F.R.S. 
‘INDIVIDUAL PSYCHOLOGY, by Alfred Adler 
-v MATHEMATICS FOR PHILOSOPHERS, by G. H. Hardy, 

F.R.S. 

•THE PSYCHOLOGY OF MYTHS, by G. Elliot Smith, F.R.S. 

THE PHILOSOPHY OF THE UNCONSCIOUS by E. von 
Hartmann. Introduction by Prof. G. Elliot Smith 
THE THEORY OF MEDICAL DIAGNOSIS, by F. G. Crook- 
shank, M.D., F.R.C.P. 

THE ELEMENTS OF PSYCHOTHERAPY, by William Brown, 

M.D., D.Sc. 

'EMOTION AND INSANITY, by S. Thalbitzer. Introduction 
by Prof. H. Hof ding 

THE LAWS OF FEELING, by F. Paulhan 

‘THE PSYCHOLOGY OF MUSIC, by Edward J. Dent 

‘COLOUR-HARMONY, by James Wood 

‘THE DEVELOPMENT OF CHINESE THOUGHT, by Liang 
Che Chiao 

THE HISTORY OF MATERIALISM, by F. A. Lange 
•PSYCHE, by E. Rohde 

THE PRIMITIVE MIND, by P. Radin, Ph.D. 

'THE PSYCHOLOGY OF PRIMITIVE PEOPLES, by B. Ma¬ 
linowski, Ph.D., D.Sc. 

‘THE STATISTICAL METHOD IN ECONOMICS, by P. 
Sargant Florence 

THE PRINCIPLES OF CRITICISM, by I. A. Richards 
5THE PHILOSOPHY OF ‘AS IF’ by H. Vaihinger 


CHANCE, LOVE, AND LOGIC 


PHILOSOPHICAL ESSAYS 

BY THE LATE 

CHARLES S. PEIRCE 

THE FOUNDER OF PRAGMATISM 


EDITED WITH AN INTRODUCTION 
BY 

MORRIS R. COHEN 


WITH A SUPPLEMENTARY ESS4F ON 
THE PRAGMATISM OF PEIRCE 

BY 

JOHN DEWEY 




NEW YORK 

HARCOURT, BRACE & COMPANY, INC. 

LONDON: KEGAN PAUL TRENCH, TRUBNER & CO., LTD.. 

1923 




COPYRIGHT, 1923, BY 
HARCOURT, BRACE AND COMPANY, INC. 


PRINTED IN THE U. S. A. 



;1A711575 


TABLE OF CONTENTS 


PAGE 

Introduction .vii 

Proem. The Rules of Philosophy . i 

Part I. Chance and Logic (Illustrations of the Logic 
of Sgence.) 

1 . The Taxation of Belief. 7 

2 . How to Make Our Ideas Clear.32 

3 . The Doctrine of Chances.61 

4 . The Probability of Induction.82 

5 . The Order of Nature.106 

6. Deduction, Induction and Hypothesis.131 

Part II. Love and Chance 

1. The Architecture of Theories.157 

2 . The Doctrine of Necessity Examined.179 

3 . The Law of Mind.202 

4 . Man’s Glassy Essence.23S 

5 . Evolutionary Love.267 

Supplementary Essay — The Pragmatism of Peirce, 

by John Dewey.301 































/ 














PREFACE £ 

In the essays gathered together in this volume we have 
the most developed and coherent available account of the 
philosophy of Charles S. Peirce, whom James, Royce, 
Dewey, and leading thinkers in England, France, Ger¬ 
many and Italy have placed in the forefront of the great 
seminal minds of recent times. Besides their inherent 
value as the expression of a highly original and fruitful 
mind, unusually well trained and informed in the exact 
sciences, these essays are also important as giving us the 
sources of a great deal of contemporary American philoso¬ 
phy. Because of this historical importance no omissions 
or changes have been made in the text beyond the correc¬ 
tion of some obvious slips and the recasting of a few ex¬ 
pressions in the interest of intelligibility. . 

In a sub J' ect which bristles with suggestions and diffi¬ 
culties the temptation to add notes of explanation or dis¬ 
sent is almost insuperable. But as such notes might easily 
have doubled the size of this volume I have refrained from 
all comment on the text except in a few footnotes (indi¬ 
cated, as usual, in brackets). The introduction is intended 
(and I hope it will) help the reader to concatenate the 
various lines of thought contained in these essays. I can¬ 
not pretend to have adequately indicated their significance. 

Great minds like those of James and Royce have been 
nourished by these writings and I am persuaded that they 


/ 

/ 

I 


III 


iv 


PREFACE 


still offer mines of fruitful suggestion. Prof. Dewey’s sup¬ 
plementary essay indicates their value for the fundamental 
question of metaphysics, viz. the nature of reality. 

Grateful acknowledgment is here made to Mrs. Paul 
Cams and to the Open Court Publishing Co. for permission 
to reprint the essays of Part II from the Monist. The late 
Paul Cams was one of the very few who not only gave 
Peirce an opportunity to publish, but publicly recognized 
the importance of his writings. 

I must also acknowledge my obligation to Professor 
Dewey for kind permission to reprint his essay on the 
Pragmatism of Peirce from the Journal of Philosophy, and 
to the editors of that Journal, Professors Woodbridge and 
Bush, for permission to reprint some material of my own. 
Part V of the Bibliography was compiled by Mr. Irving 
Smith. 

Morris R. Cohen 

The College or the City of New York. 


\ 


\ 


( 


> 


INTRODUCTION 


Many and diverse are the minds that form the philo¬ 
sophic community. There are, first and foremost, the great 
masters, the system builders who rear their stately palaces 
towering to the moon. These architectonic minds are 
served by a varied host of followers and auxiliaries. Some 
provide the furnishings to make these mystic mansions of 
the mind more commodious, while others are engaged in 
making their fagades more imposing. Some are busy 
strengthening weak places or building much-needed addi¬ 
tions, w T hile many more are engaged in defending these 
structures against the impetuous army of critics who are 
ever eager and ready to pounce down upon and destroy all 
that is new or bears the mortal mark of human imperfec¬ 
tion. There are also the philologists, those who are in a 
more narrow sense scholars, who dig not only for facts or 
roots, but also for the stones which may serve either for 
building or as weapons of destruction. Remote from all 
these, however, are the intellectual rovers who, in their 
search for new fields, venture into the thick jungle that 
surrounds the little patch of cultivated science. They are 
not gregarious creatures, these lonely pioneers; and in their 
wanderings they often completely lose touch with those 
who tread the beaten paths. Those that return to the com¬ 
munity often speak strangely of strange things; and it is 
not always that they arouse sufficient faith for others to 
follow them and change their trails into high roads. 


Vll 


V1U 


INTRODUCTION 


Few nowadays question the great value of these pioneer 
minds; and it is often claimed that universities are estab¬ 
lished to facilitate their work, and to prevent it from being 
lost. But universities, like other well-managed institutions, 
can find place only for those who work well in harness. 
The restless, impatient minds, like the socially or conven¬ 
tionally unacceptable, are thus kept out, no matter how 
fruitful their originality. Charles S. Peirce was certainly 
one of these restless pioneer souls with the fatal gift of 
genuine originality. In his early papers, in the Journal of 
Speculative Philosophy , and later, in the Monist papers 
reprinted as Part II of this volume, we get glimpses of a 
vast philosophic system on which he was working with an 
unusual wealth of material and apparatus. To a rich 
imagination and extraordinary learning he added one of the 
most essential gifts of successful system builders, the power 
to coin an apt and striking terminology. But the admitted 
incompleteness of these preliminary sketches of his philo¬ 
sophic system is not altogether due to the inherent difficulty 
of the task and to external causes such as neglect and 
poverty. A certain inner instability or lack of self-mas¬ 
tery is reflected in the outer moral or conventional way¬ 
wardness which, except for a few years at Johns Hopkins, 
caused him to be excluded from a university career, and 
thus deprived him of much needed stimulus to ordinary 
consistency and intelligibility. As the years advanced, 
bringing little general interest in, or recognition of, the bril¬ 
liant logical studies of his early years, Peirce became more 
and more fragmentary, cryptic, and involved; so that 
James, the intellectual companion of his youth, later found 


t 


INTRODUCTION 


IX 


his lectures on pragmatism, “ flashes of brilliant light re¬ 
lieved against Cimmerian darkness ” — a statement not to 
be entirely discounted by the fact that James had no inter¬ 
est in or aptitude for formal logical or mathematical con¬ 
siderations. 

Despite these limitations, however, Peirce stands out as 

v * ■ / v/-- ■ 

one of the great founders of modern scientific logic; and in 
the realm of general philosophy the development of some 
of his pregnant ideas has led to the pragmatism and 
radical empiricism of James, as well as to the mathematical 
idealism of Royce, and to the anti-nominalism which char¬ 
acterizes the philosophic movement known as Neo-Realism. 
At any rate, the work of James, Royce, and Russell, as 
well as that of logicians like Schroeder, brings us of the 
present generation into a better position to appreciate the 
significance of Peirce’s work, than were his contemporaries. 

I 

Peirce was by antecedents, training, and occupation a 
scientist. He was a son of Benjamin Peirce, the great 
Harvard mathematician, and his early environment, to¬ 
gether with his training in the Lawrence Scientific School, 
justified his favorite claim that he was brought up in a 
laboratory. He made important contributions not only in 
mathematical logic but also in photometric astronomy, 
geodesy, and psychophysics, as well as in philology. For 
many years Peirce worked on the problems of geodesy, and 
his contribution to the subject, his researches on the pendu¬ 
lum, was at once recognized by European investigators 
in this field. The International Geodetic Congress, to 


X 


INTRODUCTION 


which he was the first American representative, gave un¬ 
usual attention to his paper, and men like Cellerier and 
Plantamour acknowledged their obligations to him. 1 

This and other scientific work involving fine measure¬ 
ment, with the correlative investigations into the theory 
of probable error, seem to have been a decisive influence 
in the development of Peirce’s philosophy of chance. 
Philosophers inexperienced in actual scientific measurement 
may naively accept as absolute truth such statements as 
“ every particle of matter attracts every other particle 
directly as the product of their masses and inversely as the 
square of the distance,” or “when hydrogen and oxygen 
combine to form water the ratio of their weights is 1:8.” 
But to those who are actually engaged in measuring natural 
phenomena with instruments of precision, nature shows no 
such absolute constancy or simplicity. As every laboratory 
worker knows, no two observers, and no one observer in 
successive experiments, get absolutely identical results. To 
the men of the heroic period of science this was no difficulty. 
They held unquestioningly the Platonic faith that nature 
was created on simple geometric lines, and all the minute 
variations were attributable to the fault of the observer or 
the crudity of his instruments. This heroic faith was, 
and still is, a most powerful stimulus to scientific research 
and a protection against the incursions of supernaturalism. 
But few would defend it to-day in its explicit form, and 
there is little empirical evidence to show that while the 
observer and his instruments are always varying, the ob- 

1 See Plantamour’s “ Recherches Experim&nlales sur le mouvettient 
simultane d’un pcndulc et de ses supports ” Geneva, 1878, pp. 3-4. 


INTRODUCTION 


X! 


jects which he measures never deviate in the slightest from 
the simple law. Doubtless, as one becomes more expert in 
the manipulation of physical instruments, there is a notice¬ 
able diminution of the range of the personal “ error,” but 
no amount of skill and no refinement of our instru¬ 
ments have ever succeeded in eliminating irregular, though 
small, variations. “Try to verify any law of nature and 
you will find that the more precise your observations, the 
more certain they will be to show irregular departure from 
the law.” 2 There is certainly nothing in our empirical in¬ 
formation to prevent us from saying that all the so-called 
constants of nature are merely instances of variation be¬ 
tween limits so near each other that their differences 
may be neglected for certain purposes. Moreover, the ap¬ 
proach to constancy is observed only in mass phenomena, 
when we are dealing with very large numbers of particles; 
but social statistics also approach constant ratios when 
the numbers are very large. Hence, without denying dis¬ 
crepancies due solely to errors of observation, Peirce con¬ 
tends that “ we must suppose far more minute discrepancies 
to exist owing to the imperfect cogency of the law itself, 
to a certain swerving of the facts from any definite 
formula.” 

It is usual to associate disbelief in absolute laws of na¬ 
ture with sentimental claims for freedom or theological 
miracles. It is, therefore, well to insist that Peirce’s attack 
is entirely in the interests of exact logic and a rational 
account of the physical universe. As a rigorous logician 
familiar with the actual procedures by which our knowledge 


2 P. 190. 


3 pp. 162-163. 


INTRODUCTION 


• » 

XII 

of the various laws of nature is obtained, he could not 
admit that experience could prove their claim to absolute¬ 
ness. All the physical laws actually known, like Boyle’s 
law or the law of gravitation, involve excessive simplifica¬ 
tion of the phenomenal course of events, and thus a large 
element of empirical inaccuracy. But a more positive 
objection against the traditional assumption of absolute or 
invariable laws of nature, is the fact that such assumption 
makes the regularities of the universe ultimate, and thus 
cuts us off from the possibility of ever explaining them or 
how there comes to be as much regularity in the universe 
as there is. But in ordinary affairs, the occurrence of any 
regularity is the very thing to be explained. Moreover, 
modern statistical mechanics and thermodynamics (theory 
of gases, entropy, etc.) suggest that the regularity in the 
universe is a matter of gradual growth; that the whole of 
physical nature is a growth from a chaos of diversity to a 
maximum of uniformity or entropy. A leading physicist of 
the 19th Century, Boltzmann, has suggested that the 
process of the whole physical universe is like that of a 
continuous shaking up of a hap-hazard or chance mixture 
of things, which thus gradually results in a progressively 
more uniform distribution. Since Duns Scotus, students 
of logic have known that every real entity has its individual 
character (its haecceitas or thisness ) which cannot be ex¬ 
plained or deduced from that which is uniform. Every 
explanation, for example, of the moon’s path must take 
particular existences for granted. Such original or unde¬ 
rived individuality and diversity is precisely what Peirce 
means by chance; and from this point of view chance is 
prior to law. 


INTRODUCTION 


XIII 


a 

All that is necessary to visualize this is to suppose that 
there is an infinitesimal tendency in things to acquire 
habits, a tendency which is itself an accidental variation 
grown habitual. We shall then be on the road to explain 
the evolution and existence of the limited uniformities 
actually prevailing in the physical world. 

A good deal of the foregoing may sound somewhat 
mythologic. But even if it were so it would have the merit 
of offering a rational alternative to the mechanical mythol¬ 
ogy according to which all the atoms in the universe are 
to-day precisely in the same condition in which they were 
on the day of creation, a mythology which is forced to 
regard all the empirical facts of spontaneity and novelty 
as illusory, or devoid of substantial truth. 

The doctrine of the primacy of chance naturally suggests 
the primacy of mind. Just as law is a chance habit so is 
matter inert mind. The principal law of mind is that ideas 
literally spread themselves continuously and become more 
and more general or inclusive, so that people who form 
communities of any sort develop general ideas in common. 
When this continuous reaching-out of feeling becomes nur¬ 
turing love, such, e.g., which parents have for their off¬ 
spring or thinkers for their ideas, we have creative 
# 

evolution. 

James and Royce have called attention to the similarity 
between Peirce’s doctrine of tychistic-agapism (chance and 
love) and the creative evolution of Bergson. But while 
both philosophies aim to restore life and growth in their 
account of the nature of things, Peirce’s approach seems to 
me to have marked advantages, owing to its being in closer 


XIV 


INTRODUCTION 


touch with modern physics. Bergson’s procedure is largely 
based on the contention that mechanics cannot explain 
certain empirical facts, such as the supposed identity of 
the vertebrate eye and the eye of the scallop. But the fact 
here is merely one of a certain resemblance of pattern, which 
may well be explained by the mechanical principles of con¬ 
vergent evolution. Peirce’s account involves no rejection 
of the possibility of mechanical explanations. Indeed, by 
carrying chance into the laws of mechanics he is enabled to 
elaborate a positive and highly suggestive theory of proto¬ 
plasm to explain the facts of plasticity and habit. 4 Instead 
of postulating with Spencer and Bergson a continuous 
growth of diversity, Peirce allows for growth of habits both 
in diversity and in uniformity. The Spencerian mechanical 
philosophy reduces all diversity to mere spatial differences. 
There can be no substantial novelty; only new forms or 
combinations can arise in time. The creative evolution of 
Bergson though intended to support the claims of spon¬ 
taneity is still like the Spencerian in assuming all evolution 
as proceeding from the simple to the complex. Peirce 
allows for diversity and specificity as part of the original 
character or endowment of things, which in the course of 
time may increase in some respects and diminish in others. 
Mind acquires the habit both of taking on, and also of lay¬ 
ing aside, habits. Evolution may thus lead to homogeneity 
or uniformity as well as to greater heterogeneity. 

Not only has Peirce a greater regard than even Bergson 
for the actual diversity and spontaneity of things, but he 
is in a much better position than any other modern phi- 


4 Pp. 249 ff. 


INTRODUCTION 


xv 


losopher to explain the order and coherence of the world. 
This he effects by uniting the medieval regard for the 
reality of universals with the modern scientific use of the 
concept of continuity. The unfortunate war between the 
pioneers of modern science and the adherents of the scho¬ 
lastic doctrine of substantial forms, has been one of the 
great misfortunes of human thought, in that it made abso¬ 
lute atomism and nominalism the professed creed of physi¬ 
cal science. Now, extreme nominalism, the insistence on 
the reality of the particular, leaves no room for the genuine 
reality of law. It leaves, as Hume had the courage to 
admit, nothing whereby the present can determine the 
future; so that anything is as likely to happen as not. 
From such a chaotic world, the procedure of modern natural 
and mathematical science has saved us by the persistent 
use of the principle of continuity; and no one has indicated 
this more clearly than Peirce who was uniquely qualified 
to do so by being a close student both of Duns Scotus and 
of modern scientific methods. 

It is instructive in this respect to contrast the views of 
Peirce and James. James, who so generously indicated his 
indebtedness to Peirce for his pragmatism, was also largely 
indebted to Peirce for his doctrine of radical empiricism. 5 
The latter doctrine seeks to rescue the continuity and 
fluidity of experience from the traditional British empiri¬ 
cism or nominalism, which had resolved everything into a 
number of mutually exclusive mental states. It is curious, 
however, that while in his psychology James made extensive 
use of the principle of continuity, he could not free himself 

6 James, Pluralistic Universe, pp. 398-400. 


INTRODUCTION 


xvi 

from British nominalism in his philosophy — witness the 
extreme individualism of his social philosophy or the equally 
extreme anthropomorphism of his religion. Certain of 
Peirce’s suggestions as to the use of continuity in social 
philosophy have been developed by Royce in his theory of 
social consciousness and the nature of the community; 6 
but much remains to be worked out and we can but repeat 
Peirce’s own hope: “ May some future student go over 
this ground again and have the leisure to give his results 
to the world.” 

It is well to note, however, that after writing the papers 
included in this volume Peirce continued to be occupied 
with the issues here raised. This he most significantly 
indicated in the articles on logical topics contributed to 
Baldwin’s Dictionary of Philosophy. 7 

In these articles it is naturally the logical bearing of the 
principles of tychism (chance), synechism (continuity), and 
agapism (love) that is stressed. To use the Kantian ter¬ 
minology, almost native to Peirce, the regulative rather 
than the constitutive aspect of these principles is empha¬ 
sized. Thus the doctrine of chance is not only what it was 
for James’ radical empiricism, a release from the blind 
necessity of a “ block universe,” but also a method of keep- 

6 Royce, Studies in Good and Evil, and The Problem of Christianity, 
esp. Vol. 2. Baldwin ( Mental Development) is heavily indebted to Royce 
in this respect. 

7 These articles are by-products or fragments of a comprehensive work 
on Logic on which Peirce was engaged for many years. For the writing 
of this book, Royce declared, no greater mind or greater erudition has 
appeared in America. Only several chapters seem to have been finished, 
and will doubtless be included with other hitherto unpublished manu¬ 
scripts in the complete edition of Peirce’s writings that is now being 
prepared by Harvard University. 


INTRODUCTION 


xv ii 

ing open a possible explanation of the genesis of the laws 
of nature and an interpretation of them in accordance with 
the theorems of probability, so fruitful in physical science 
as well as in practical life. So the doctrine of love is not 
only a cosmologic one, showing how chance feeling generates 
order or rational diversity through the habit of generality 
or continuity, but it also gives us the meaning of truth in 
social terms, in showing that the test as to whether any 
proposition is true postulates an indefinite number of co¬ 
operating investigators. On its logical side the doctrine of 
love (agapism) also recognized the important fact that 
general ideas have a certain attraction which makes us divine 
their nature even though we cannot clearly determine their 
precise meaning before developing their possible conse¬ 
quences. 

Of the doctrine of continuity we are told expressly 8 that 
“ synechism is not an ultimate absolute metaphysical 
doctrine. It is a regulative principle of logic,” seeking the 
thread of identity in diverse cases and avoiding hypotheses 
that this or that is ultimate and, therefore, inexplicable. 
(Examples of such hypotheses are: the existence of abso¬ 
lutely accurate or uniform laws of nature, the eternity and 
absolute likeness of all atoms, etc.) To be sure, the 
synechist cannot deny that there is an element of the in¬ 
explicable or ultimate, since it is directly forced upon him. 
But he cannot regard it as a source of explanation. The 
assumption of an inexplicability is a barrier on the road to 
science. “The form under which alone anything can be 
understood is the form of generality which is the same thing 

8 Baldwin’s Dictionary, article Synechism. 


XVI11 


INTRODUCTION 


as continuity .” 9 This insistence on the generality of 
intelligible form is perfectly consistent with due emphases 
on the reality of the individual, which to a Scotist realist 
connotes an element of will or will-resistence, but in logical 
procedure means that the test of the truth or falsity of any 
proposition refers us to particular perceptions . 10 But 
as no multitude of individuals can exhaust the meaning of 
a continuum, which includes also organizing relations of 
order, the full meaning of a concept cannot be in any 
individual reaction, but is rather to be sought in the manner 
in which all such reactions contribute to the development of 
the concrete reasonableness of the whole evolutionary 
process. In scientific procedure this means that integrity 
of belief in general is more important than, because it is 
the condition of, particular true beliefs. 

II 

This insistence on the continuity so effectually used as a 
heuristic principle in natural and mathematical science, 
distinguishes the pragmatism of Peirce from that of his 
follower James. Prof. Dewey has developed this point 
authoritatively in the supplementary essay; but in view of 
the general ignorance as to the sources of pragmatism which 
prevails in this incurious age, some remarks on the actual 
historical origin of pragmatism may be in order. 

There can be little doubt that Peirce was led to the formu¬ 
lation of the principle of pragmatism through the influence 

9 lb. 

10 Baldwin’s Dictionary, art. Individual: “ Everything whose identity 
consists in a continuity of reactions will be a single logical individual.” 


INTRODUCTION 


xix 


of Chauncey Wright . 11 Wright who had first hand ac¬ 
quaintance with creative scientific work in mathematics, 
physics, and botany was led by the study of Mill and Bain 
to reflect on the characteristics of scientific method. This 
reflection led him to draw a distinction between the use of 
popular scientific material, by men like Spencer, to con¬ 
struct a myth or picture of the world, and the scientific 
use of laws by men like Newton as means for extending our 
knowledge of phenomena. Gravitation as a general fact 
had interested metaphysicians long before Newton. What 
made Newton’s contribution scientific was the formulation 
of a mathematical law which has enabled us to deduce all 
the then known facts of the solar system and to anticipate 
or predict many more facts the existence of which would 
not otherwise be even suspected, e.g., the existence of the 
planet Neptune. Wright insists, therefore, that the prin¬ 
ciples of modern mathematical and physical science are 
the means through which nature is discovered, that scientific 


11 The personal relations between Peirce and Wright were thus de¬ 
scribed by Peirce in a letter to Mrs. Ladd-Franklin (Journal of Philosophy 
Vol. 13, p. 719): “It must have been about 1857 when X first made 
the acquaintance of Chauncey Wright, a mind about on the level of 
J. S. Mill, He was a thorough mathematician. He had a most pene¬ 
trating intellect. — He and I used to have long and very lively and close 
disputations lasting two or three hours daily for many years. In the 
sixties I started a little club called ‘The Metaphysical Club.’ —Wright 
was the strongest member and probably I was next. — Then there were 
Frank Abbott, William James and others.” “It was there that the name 
and the doctrine of pragmatism saw the light.” It might be added that 
Peirce’s tychism is indebted to Wright’s doctrine of accidents and “ cosmic 
weather,” a doctrine which maintained against LaPlace that a mind know¬ 
ing nature from moment to moment is bound to encounter genuine novelty 
in phenomena, which no amount of knowledge would enable us to foresee. 
See Wright’s Philosophical Discussions —1876, also Cambridge Hist, of 
American Literature, Vol. 3, p. 234. 


XX 


INTRODUCTION 


laws are the finders rather than merely the summaries of 
factual truths. This conception of the experimental scien¬ 
tist as translating general propositions into prescriptions 
for attaining new experimental truths, is the starting point 
of Peirce's pragmatism. The latter is embodied in the 
principle that the meaning of a concept is to be found in 
“ all the conceivable experimental phenomena which the 
affirmation or denial of the concept could imply.” 12 

In the earlier statement of the pragmatic maxim , 13 
Peirce emphasized the consequences for conduct that follow 
from the acceptance or rejection of an idea; but the stoical 
maxim that the end of man is action did not appeal to him 
as much at sixty as it did at thirty . 14 Naturally also Peirce 
could not follow the development of pragmatism by Wm. 
James who, like almost all modern psychologists, was a 
thorough nominalist and always emphasized particular 
sensible experience . 15 It seemed to Peirce that such em* 


12 Alonist, Vol. is, p. 1S0. 

13 This volume, pp. 43-45. 

34 “To say that we live for the sake of action would be to say that 
there is no such thing as a rational purport/’ Monist, Vol. XV, p. 175. 

16 The letter to Mrs. Ladd-Franklin quoted before, explains why 
James, though always loyal to Peirce and anxious to give him credit when¬ 
ever possible, could not understand the latter’s lectures on pragmatism. 
Peirce’s incidental judgments on others is worth quoting here: 

“ Modem psycholoigsts are so soaked with sensationalism that they 
cannot understand anything that does not mean that. How can I, to 
whom nothing seems so thoroughly real as generals, and who regards 
Truth and Justice as literally the most powerful powers in the world, 
expect to be understood by the thoroughgoing Wundtian? But the curious 
thing is to see absolute idealists tainted with this disease, — or men who, 
like John Dewey, hover between Absolute Idealism and Sensationalism. 
Royce’s opinions as developed in his World and Individualism are ex¬ 
tremely near to mine. His insistence on the elements of purpose in 
intellectual concepts is essentially the pragmatic position.” 


INTRODUCTION 


XXI 


phasis on particular experiences endangered the principle 
of continuity which in the hands of men like Weierstrass 
had reformed modern mathematics. For this reason he 
began to call his own doctrine pragmaticism, a sufficiently 
unattractive name, he thought, to save it from kidnappers 
and from popularity. He never, however, abandoned the 
principle of pragmatism, that the meaning of an idea is 
clarified (because constituted) by its conceivable experi¬ 
mental consequences. Indeed, if we want to clarify the 
meaning of the idea of pragmatism, let us apply the prag¬ 
matic test to it. What will be the effect of accepting it? 
Obviously it will be to develop certain general ideas or 
habits of looking at things. 

Peirce's pragmatism has, therefore, a decidedly intel¬ 
lectual cast. The meaning of an idea or proposition is 
found not by an intuition of it but by working out its im¬ 
plications. It admits that thought does not constitute 
reality. Categories can have no concrete being without 
action or immediate feeling. But thought is none the less 
an essential ingredient of reality; thought is “ the melody 
running through the succession of our sensations.” Prag- 

" i 

matism, according to Peirce, seeks to define the rational 
purport, not the sensuous quality. It is interested not in 
the effect of our practical occupations or desires on our 
ideas, but in the function of ideas as guides of action. 
Whether a man is to pay damages in a certain lawsuit may 
depend, in fact, on a term in the Aristotelian logic such as 
proximate cause. 

It is of interest to observe that though Peirce is an ardent 
admirer of Darwin's method, his scientific caution makes 


INTRODUCTION 


Xlii 

him refuse to apply the analogy of biologic natural selec¬ 
tion to the realm of ideas, in the wholesale and uncritical 
manner that has lately become fashionable. Natural selec¬ 
tion may well favor the triumph of views which directly 
influence biologic survival. But the pleasure of entertain¬ 
ing congenial illusions may overbalance the inconvenience 
resulting from their deceptive character. Thus rhetorical 
appeals may long prevail over scientific evidence. 

Ill 

Peirce preferred to call himself a logician, and his con¬ 
tributions to logic have so far proved his most generally 
recognized achievement. For a right perspective of these 
contributions we may well begin with the observation that 
though few branches of philosophy have been cultivated as 
continuously as logic, Kant was able to affirm that the 
science of logic had made no substantial progress since the 
time of Aristotle. The reason for this is that Aristotle’s 
logic, the logic of classes, was based on his own scientific 
procedure as a zoologist, and is still in essence a valid 
method so far as classification is part of all rational pro¬ 
cedure. But when we come to describe the mathematical 
method 'of physical science, we cannot cast it into the 
Aristotelian form without involving ourselves in such com¬ 
plicated artificialities as to reduce almost to nil the value 
of Aristotle’s logic as an organon. Aristotle’s logic enables 
us to make a single inference from two premises. But the 
vast multitude of theorems that modern mathematics has 
derived from a few premises as to the nature of number, 
shows the need of formulating a logic or theory of inference 


INTRODUCTION 


xxiii 


that shall correspond to the modern, more complicated, prac¬ 
tice as Aristotle’s logic did to simple classifkatory zoology. 
To do this effectively would require the highest construc¬ 
tive logical genius, together with an intimate knowledge 
of the methods of the great variety of modern sciences. 
This is in the nature of the case a very rare combination, 
since great investigators are not as critical in examining 
their own procedure as they are in examining the subject 
matter which is their primary scientific interest. Hence, 
when great investigators like Poincare come to describe 
their own work, they fall back on the uncritical assumptions 
of the traditional logic which they learned in their school 
days. Moreover, “ For the last three centuries thought 
has been conducted in laboratories, in the field, or otherwise 
in the face of the facts, while chairs of logic have been 
filled by men who breathe the air of the seminary.” 10 The 
great Leibnitz had the qualifications, but here, as else¬ 
where, his worldly occupations left him no opportunity 
except for very fragmentary contributions. It was not until 
the middle of the 19th century that two mathematicians, 
Boole and DeMorgan, laid the foundations for a more gen¬ 
eralized logic. Boole developed a general logical algorithm 
or calculus, while DeMorgan called attention to non-syllogis- 
tic inference and especially to the importance of the logic of 
relations. Peirce’s great achievement is to have recognized 
the possibilities of both and to have generalized and de¬ 
veloped them into a general theory of scientific inference. 
The extent and thoroughness of his achievement has been 
obscured by his fragmentary way of writing and by a rather 


16 Baldwin’s Dictionary, art. Method. 


xxiv 


INTRODUCTION 


unwieldy symbolism. Still, modern mathematical logic, 
such as that of Russell’s Principles of Mat hematic s f is but a 
development of Peirce’s logic of relatives. 

This phase of Peirce’s work is highly technical and an 
account of it is out of place here. Such an account will 
be found in Lewis’ Survey of Symbolic Logic . 17 I refer to 
it here only to remind the reader that the Illustrations of 
the Logic of the Sciences (Part I of this volume) have a 
background of patient detailed work which is still being 
developed to-day. 

Symbolic logic has been held in rather low esteem by 
the followers of the old classical methods in philosophy. 
Their stated objection to it has been mainly that it is 
concerned with the minutiae of an artificial language and is 
of no value as a guide to the interpretation of reality. 
Now it should be readily admitted that preoccupation with 
symbolic logic is rather apt to retard the irresponsible 
flight of philosophic fancy. Yet this is by no means always 
an evil. By insisting on an accuracy that is painful to those 
impatient to obtain sweeping and comforting, though hasty, 
conclusions, symbolic logic is well calculated to remove the 
great scandal of traditional philosophy — the claim of abso¬ 
lutely certain results in fields where there is the greatest 
conflict of opinion. This scandalous situation arises in part 
from the fact that in popular exposition we do not have to 
make our premises or assumptions explicit; hence all sorts 
of dubious prejudices are implicitly appealed to as abso- 

17 “ Peirce anticipated the most important procedures of his successors 
even when he did not work them out himself. Again and again one finds 
the clue to the most recent developments in the writings of Peirce,” 
Lewis’ Survey of Symbolic Logic, p. 79. 


INTRODUCTION 


XXV 


lutely necessary principles. Also, by the use of popular 
terms which have a variety of meanings, one easily slides 
from one meaning to another, so that the most improbable 
conclusions are thus derived from seeming truisms. By 
making assumptions and rules explicit, and by using tech¬ 
nical terms that do not drag wide penumbras of meaning 
with them, the method of symbolic logic may cruelly reduce 
the sweeping pretensions of philosophy. But there is no 
reason for supposing that pretentiousness rather than 
humility is the way to philosophic salvation. Man is bound 
to speculate about the universe beyond the range of his 
knowledge, but he is not bound to indulge the vanity of 
setting up such speculations as absolutely certain dogmas. 

There is, however, no reason for denying that greater 
rigor and accuracy of exposition can really help us to dis¬ 
cern new truth. Modern mathematics since Gauss and 
Weierstrass has actually been led to greater fruitfulness by 
increased rigor which makes such procedure as the old 
proofs of Taylor's theorem no longer possible. The sub¬ 
stitution of rigorous analytic procedures for the old Eu¬ 
clidean proofs based on intuition, has opened up vast fields 
of geometry. Nor has this been without any effect on 
philosophy. Where formerly concepts like infinity and con¬ 
tinuity were objects of gaping awe or the recurrent occa¬ 
sions for intellectual violence, 18 we are now beginning to 
use them, thanks to Peirce and Royce, in accurate and 
definable senses. Consider, for instance, the amount of 
a priori nonsense which Peirce eliminates by pointing out 

18 Hans Breitmann is symbolic of those who “ solved the infinite as one 
eternal sphere.” 


XXVI 


INTRODUCTION 


that the application of the concept of continuity to a span 
of consciousness removes the necessity for assuming a first 
or last moment; so likewise the range of vision on a large 
unobstructed ground has no line between the visible and the 
invisible. These considerations will be found utterly de¬ 
structive of the force of the old arguments (fundamental 
to Kant and others) as to the necessary infinity of time and 
space. Similar enlightenment is soon likely to result from 
the more careful use of terms like relative and absolute, 
which are bones of contention in philosophy but Ariadne 
threads of exploration in theoretical physics, because of 
the definite symbolism of mathematics. Other important 
truths made clear by symbolic logic is the hypothetical 
character of universal propositions and the consequent in¬ 
sight that no particulars can be deduced from universals 
alone, since no number of hypotheses can without given data 
establish an existing fact. 

There is, however, an even more positive direction in 
which symbolic logic serves the interest of philosophy, and 
that is in throwing light on the nature of symbols and on 
the relation of meaning. Philosophers have light-heartedly 
dismissed questions as to the nature of significant signs as 
‘ merely ’ (most fatal word!) a matter of language. But 
Peirce in the paper on Man’s Glassy [Shakespearian for 
Mirror-Like] Essence, endeavors to exhibit man’s whole 
nature as symbolic. 19 This is closely connected with his 
logical doctrine which regards signs or symbols as one of 

19 See Journal of Speculative Philosophy , Vol. 2, pp. 155-157, artide on 
A New List of Categories in the Proceedings of the American Academy 
of Arts and Sciences, Vol. 7, 287-298 and article on Sign, in Baldwin’s 
Dictionary. 


INTRODUCTION 


xxv ii 

the fundamental categories or aspects of the universe 
(Thoughts and things are the other two). Independently 
of Peirce but in line with his thought another great and 
neglected thinker, Santayana, has shown that the whole life 
of man that is bound up with the institutions of civilization, 
is concerned with symbols. 

It is not altogether accidental that, since Boole and 
DeMorgan, those who have occupied themselves with sym¬ 
bolic logic have felt called upon to deal with the problem 
of probability. The reason is indicated by Peirce when he 
formulates the problem of probable inference in such a way 
as to make the old classic logic of absolutely true or false 
conclusions, a limiting case (i.e., of values i and o) of the 
logic of probable inference whose values range all the way 
between these two limits. This technical device is itself 
the result of applying the principle of continuity to throw 
two hitherto distinct types of reasoning into the same class. 
The result is philosophically significant. 

Where the classical logic spoke of major and minor 
premises without establishing any really important dif¬ 
ference between the two, Peirce draw r s a distinction between 
the premises and the guiding principle of our argument. 
All reasoning is from some concrete situation to another. 
The propositions which represent the first are the premises 
in the strict sense of the word. But the feeling that certain 
conclusions follow from these premises is conditioned by an 
implicit or explicit belief in some guiding principle which 
connects the premises and the conclusions. When such a 
leading principle results in true conclusions in all cases of 
true premises, we have logical deduction of the orthodox 


xxviii INTRODUCTION 

type. If, however, such a principle brings about a true con¬ 
clusion only in a certain proportion of cases, then we have 
probability. 

This reduction of probability to the relative frequency 
of true propositions in a class of propositions, was suggested 
to Peirce by Venn’s Logic of Chance . Peirce uses it to 
establish some truths of greatest importance to logic and 
philosophy. 

He eliminates the difficulties of the old conceptualist 
view, which made probability a measure of our ignorance 
and yet had to admit that almost all fruitfulness of our 
practical and scientific reasoning depended on the theorems 
of probability. How could we safely predict phenomena by 
measuring our ignorance? 

Probability being reduced to a matter of the relative fre¬ 
quency of a class in a larger class or genus, it becomes, 
strictly speaking, inapplicable to single cases by themselves. 
A single penny will fall head or it will fall tail every time; 
to-morrow it will rain, or it will not rain at all. The 
probability of ^ or any other fraction means nothing in 
the single case. It is only because we feel the single event 
as representative of a class, as something which repeats 
itself, that we speak elliptically of the probability of a 
single event. Hence follows the important corollary that 
reasoning with respect to the probability of this or that ar¬ 
rangement of the universe would be valid only if universes 
were as plentiful as blackberries. 

To be useful at all, theories must be simpler than the 
complex facts which they seek to explain. Hence, it is 
often convenient to employ a principle of certainty where 



INTRODUCTION 


XXIX 


the facts justify only a principle of some degree of proba¬ 
bility. In such cases we must be cautious in accepting 
any extreme consequence of these principles, and also be 
on guard against apparent refutations based on such ex¬ 
treme consequences. 

Finally I should like to emphasize the value of Peirce’s 
theory of inference for a philosophy of civilization. To the 
old argument that logic is of no importance because people 
learn to reason, as to walk, by instinct and habit and not by 
scientific instruction, Peirce admits 20 that “ all human 
knowledge up to the highest flights of science is but the 
development of our inborn animal instincts.” But though 
logical rules are first felt implicitly, bringing them into 
explicit consciousness helps the process of analysis and 
thus makes possible the recognition of old principles in novel 
situations. This increases our range of adaptability to such 
an extent as to justify a general distinction between the 
slave of routine or habit and the freeman who can anticipate 
and control nature through knowledge of principles. Peirce’s 
analysis of the method of science as a method of attain¬ 
ing stability of beliefs by free inquiry inviting all possible 
doubt, in contrast with the methods of iteration (“will to 
believe ”) and social authority, is one of the best intro¬ 
ductions to a theory of liberal or Hellenic civilization, as 
opposed to those of despotic societies. Authority has its 
roots in the force of habit, but it cannot prevent new and 
unorthodox ideas from arising; and in the effort to defend 
authoritative social views men are apt to be far more ruth¬ 
less than in defending their own personal convictions. 


Studies in Logic, p. i8i. 


XXX 


INTRODUCTION 


IV 

Not only the pragmatism and the radical empiricism of 
James, but the idealism of Royce and the more recent 
movement of neo-realism are largely indebted to Peirce. 

It may seem strange that the same thinker should be 
claimed as foster-father of both recent idealism and realism, 
and some may take it as another sign of his lack of con¬ 
sistency. But this seeming strangeness is really due to 
the looseness with which the antithesis between realism and 
idealism has generally been put. If by idealism we denote 
the nominalistic doctrine of Berkeley, then Peirce is clearly 
not an idealist; and his work in logic as a study of types 
of order (in which Royce followed him) is fundamental 
for a logical realism. But if idealism means the old 
Platonic doctrine that “ ideas,” genera, or forms are not 
merely mental but the real conditions of existence, we need 
not wonder that Peirce was both idealist and realist. 

Royce’s indebtedness to Peirce is principally in the use 
of modern mathematical material, such as the recent de¬ 
velopment of the concepts of infinity and continuity, to 
throw light on fundamental questions of philosophy, such 
as relation of the individual to God or the Universe. At 
the end of the nineteenth century mathematics had almost 
disappeared from the repertory of philosophy (cf. Kiilpe’s 
Introduction to Philosophy ), and Peirce’s essay on the 
Law of Mind opened a new way which Royce followed in 
his World and the Individual , to the great surprise of his 
idealistic brethren. In his Problem of Christianity Royce 
has also indicated his indebtedness to Peirce for his doc- 


INTRODUCTION 


XXXI 


trine of social consciousness, the mind of the community, 
and the process of interpretation. It may be that a great 
deal of the similarity between the thoughts of these two 
men is due to common sources, such as the works of Kant 
and Schelling; but it is well to note that not only in his 
later writings but also in his lectures and seminars Royce 
continually referred to Peirce’s views. 

The ground for the neo-realist movement in American 
philosophy was largely prepared by the mathematical work 
of Russell and by the utilization of mathematics to which 
Royce was led by Peirce. The logic of Mr. Russell is 
based, as he himself has pointed out, on a combination of 
the work of Peirce and Peano. In this combination the 
notation of Peano has proved of greater technical fluency, 
but all of Peano’s results can also be obtained by Peirce’s 
method as developed by Schroeder and Mrs. Ladd-Frank- 
lin. But philosophically Peirce’s influence is far greater in 
insisting that logic is not a branch of psychology, that it 
is not concerned with merely mental processes, but with 
objective relations. To the view that the laws of logic 
represent “ the necessities of thought,” that propositions 
are true because “ we can not help thinking so,” he answers: 
“ Exact logic will say that C's following logically from A is 
a state of things which no impotence of thought alone can 
bring about.” 21 “The question of validity is purely one 
of fact and not of thinking. ... It is not in the least the 
question whether, when the premises are accepted by the 
mind, we feel an impulse to accept the conclusion also. 

21 Monist, Vol. 7, p. 27. Cf. Journal of Speculative Philosophy , 
Vol. 2, p. 207; Popular Science Monthly, Vol. 58, pp. 305-306. 


INTRODUCTION 


xxxii 

The true conclusion would remain true if we had no im¬ 
pulse to accept it, and the false one would remain false 
though we could not resist the tendency to believe in it.” 22 

Since the days of Locke modern philosophy has been 
almost entirely dominated by the assumption that one must 
study the process of knowing before one can find out the 
nature of things known; in other words, that psychology is 
the central philosophic science. The result of this has been 
an almost complete identification of philosophy with mental 
science. Nor did the influence of biologic studies of the 
middle of the nineteenth century shake the belief in that 
banal dictum of philosophic mediocrity: “ The proper 
study of mankind is man.” The recent renaissance of 
logical studies, and the remarkable progress of physics in 
our own day bid fair to remind us that while the Lockian 
way has brought some gains to philosophy, the more ancient 
way of philosophy is by no means exhausted of promise. 
Man cannot lose his interest in the great cosmic play. 
Those who have faith in the ancient and fruitful approach 
to philosophy through the doors of mathematics and physics 
will find the writings of Charles S. Peirce full of sugges¬ 
tions. That such an approach can also throw light on the 
vexed problem of knowledge needs no assurance to those 
acquainted with Plato and Aristotle. But I may conclude 
by referring to Peirce ? s doctrine of ideal as opposed to 
sensible experiment, 28 and to his treatment of the question 

22 This vol., p. 15. 

23 Suggestive for a theory of the metaphysics of fictions is the sugges¬ 
tion (p. 46) “ that the question of what would occur under circumstances 
which do not actually arise, is not a question of fact, but only of the 
most perspicuous arrangement of them.” This arrangement is, of course, 
not merely subjective. 


INTRODUCTION xxxiii 

how it is that in spite of an infinity of possible hypotheses, 
mankind has managed to make so many successful induc¬ 
tions. 24 And for the bearing of mathematical studies on the 
wisdom of life, the following is certainly worth serious re¬ 
flection: “ All human affairs rest upon probabilities. If 
man were immortal [on earth] he could be perfectly sure 
of seeing the day when everything in which he had trusted 
should betray his trust. He would break down, at last, as 
every great fortune, as every dynasty, as every civilization 
does. In place of this we have death.” The recognition 
that the death of the individual does not destroy the logical 
meaning of his utterances, that this meaning involves the 
ideal of an unlimited community, carries us into the heart 
of pure religion. 

2* P P . 128-129, cf. Monist, Vol. 7, p. 206, and Logical Studies, pp. 

175 ff. 




















CHANCE, LOVE, AND LOGIC 


PROEM 

THE RULES OF PHILOSOPHY 1 

Descartes is the father of modern philosophy, and the 
spirit of Cartesianism — that which principally distin¬ 
guishes it from the scholasticism which it displaced — may 
be compendiously stated as follows: 

1. It teaches that philosophy must begin with universal 
doubt; whereas scholasticism had never questioned funda¬ 
mentals. 

2. It teaches that the ultimate test of certainty is to be 
found in the individual consciousness; w T hereas scholasticism 
had rested on the testimony of sages and of the Catholic 
Church. 

3. The multiform argumentation of the middle ages is 
replaced by a single thread of inference depending often 
upon inconspicuous premises. 

4. Scholasticism had its mysteries of faith, but undertook 
to explain all created things. But there are many facts 
wdiich Cartesianism not only does not explain but renders 
absolutely inexplicable, unless to say that “ God makes them 
so ” is to be regarded as an explanation. 

In some, or all of these respects, most modern philoso¬ 
phers have been, in effect, Cartesians. Now without wishing 

1 From the Journal of Speculative Philosophy, vol. 2, p. 140. 


o 


PROEM 


to return to scholasticism, it seems to me that modern 
science and modern logic require us to stand upon a very 
different platform from this. 

1. We cannot begin with complete doubt. We must begin 
with all the prejudices which we actually have when we 
enter upon the study of philosophy. These prejudices are 
not to be dispelled by a maxim, for they are things which 
it does not occur to us can be questioned. Hence this 
initial skepticism will be a mere self-deception, and not real 
doubt; and no one who follows the Cartesian method will 
ever be satisfied until he has formally recovered all those 
beliefs which in form he has given up. It is, therefore, as 
useless a preliminary as going to the North Pole would be 
in order to get to Constantinople by coming down regularly 
upon a meridian. A person may, it is true, in the course 
of his studies, find reason to doubt what he began by be¬ 
lieving; but in that case he doubts because he has a positive 
reason for it, and not on account of the Cartesian maxim. 
Let us not pretend to doubt in philosophy what we do not 
doubt in our hearts. 

2. The same formalism appears in the Cartesian criterion, 
which amounts to this: “ Whatever I am clearly convinced 
of, is true.” If I were really convinced, I should have done 
with reasoning and should require no test of certainty. 
But then to make single individuals absolute judges of truth 
is most pernicious. The result is that metaphysics has 
reached a pitch of certainty far beyond that of the physical 
sciences; —only they can agree upon nothing else. In 
sciences in which men come to agreement, when a theory 


PROEM 


3 


has been broached it is considered to be on probation until 
this agreement is reached. After it is reached, the question 
of certainty becomes an idle one, because there is no one 
left who doubts it. We individually cannot reasonably 
hope to attain the ultimate philosophy which we pursue; 
we can only seek it, therefore, for the community of philoso¬ 
phers. Hence, if disciplined and candid minds carefully 
examine a theory and refuse to accept it, this ought to create 
doubts in the mind of the author of the theory himself. 

3. Philosophy ought to imitate the successful sciences in 
its methods, so far as to proceed only from tangible prem¬ 
ises which can be subjected to careful scrutiny, and to trust 
rather to the multitude and variety of its arguments than 
to the conclusiveness of any one. Its reasoning should not 
form a chain which is no stronger than its weakest link, 
but a cable whose fibers may be ever so slender, provided 
they are sufficiently numerous and intimately connected. 

4. Every unidealistic philosophy supposes some absolutely 
inexplicable, unanalyzable ultimate; in short, something 
resulting from mediation itself not susceptible of mediation. 
Now that anything is thus inexplicable, can only be known 
by reasoning from signs. But the only justification of an 
inference from signs is that the conclusion explains the fact. 
To suppose the fact absolutely inexplicable, is not to explain 
it, and hence this supposition is never allowable. 



















PART I 


CHANCE AND LOGIC 

(illustrations of the logic of science) 














CHANCE AND LOGIC 


FIRST PAPER 

THE FIXATION OF BELIEF 1 

i 

Few persons care to study logic, because everybody con¬ 
ceives himself to be proficient enough in the art of reasoning 
already. But I observe that this satisfaction is limited to 
one’s own ratiocination, and does not extend to that of 
other men. 

We come to the full possession of our power of drawing 
inferences the last of all our faculties, for it is not so much 
a natural gift as a long and difficult art. The history of 
its practice would make a grand subject for a book. The 
medieval schoolman, following the Romans, made logic the 
earliest of a boy’s studies after grammar, as being very 
easy. So it was as they understood it. Its fundamental 
principle, according to them, was, that all knowledge rests 
on either authority or reason; but that whatever is deduced 
by reason depends ultimately on a premise derived from 
authority. Accordingly, as soon as a boy was perfect in 
the syllogistic procedure, his intellectual kit of tools was 
held to be complete. 

1 Popular Science Monthly, November, 1877. 


7 


8 


CHANCE AND LOGIC 


To Roger Bacon, that remarkable mind who in the middle 
of the thirteenth century was almost a scientific man, the 
schoolmen’s conception of reasoning appeared only an ob¬ 
stacle to truth. He saw that experience alone teaches any¬ 
thing — a proposition which to us seems easy to understand, 
because a distinct conception of experience has been handed 
down to us from former generations; which to him also 
seemed perfectly clear, because its difficulties had not yet 
unfolded themselves. Of all kinds of experience, the best, 
he thought, was interior illumination, which teaches many 
things about Nature which the external senses could never 
discover, such as the transubstantiation of bread. 

Four centuries later, the more celebrated Bacon, in the 
first book of his “ Novum Organum,” gave his clear account 
of experience as something which must be open to verifica¬ 
tion and reexamination. But, superior as Lord Bacon’s 
conception is to earlier notions, a modern reader who is not 
in awe of his grandiloquence is chiefly struck by the in¬ 
adequacy of his view of scientific procedure. That we have 
only to make some crude experiments, to draw up briefs 
of the results in certain blank forms, to go through these 
by rule, checking off everything disproved and setting down 
the alternatives, and that thus in a few years physical 
science would be finished up — what an idea! “ He wrote 
on science like a Lord Chancellor,” 2 indeed. 

The early scientists, Copernicus, Tycho, Brahe, Kepler, 
Galileo and Gilbert, had methods more like those of their 
modern brethren. Kepler undertook to draw a curve 

2 [This is substantially the dictum of Harvey to John Aubrey. See 
the latter’s Brief Lives (Oxford ed. 1898) I 299]. 


THE FIXATION OF BELIEF 9 

through the places of Mars ; 3 and his greatest service to 
science was in impressing on men’s minds that this was the 
thing to be done if they wished to improve astronomy; 
that they were not to content themselves with inquiring 
whether one system of epicycles was better than another 
but that they were to sit down by the figures and find out 
what the curve, in truth, was. He accomplished this by his 
incomparable energy and courage, blundering along in the 
most inconceivable way (to us), from one irrational hy¬ 
pothesis to another, until, after trying twenty-two of these, 
he fell, by the mere exhaustion of his invention, upon the 
orbit which a mind well furnished with the weapons of 
modern logic would have tried almost at the outset . 4 

In the same way, every work of science great enough to 
be remembered for a few generations affords some 
exemplification of the defective state of the art of reasoning 
of the time when it was written; and each chief step in 
science has been a lesson in logic. It was so when Lavoisier 
and his contemporaries took up the study of Chemistry. 
The old chemist’s maxim had been, “ Lege, lege, lege, 
labora, ora, et relege.” Lavoisier’s method was not to read 
and pray, not to dream that some long and complicated 
chemical process would have a certain effect, to put it into 
practice with dull patience, after its inevitable failure to 
dream that with some modification it would have another 
result, and to end by publishing the last dream as a fact: 
his way was to carry his mind into his laboratory, and to 
make of his alembics and cucurbits instruments of thought, 

3 Not quite so, but as nearly so as can be told in a few words. 

4 [This modern logic, however, is largely the outcome of Kepler’s work.] 


10 


CHANCE AND LOGIC 


giving a new conception of reasoning as something which 
was to be done with one’s eyes open, by manipulating real 
things instead of words and fancies. 

The Darwinian controversy is, in large part, a question 
of logic. Mr. Darwin proposed to apply the statistical 
method to biology. The same thing has been done in a 
widely different branch of science, the theory of gases. 
Though unable to say what the movement of any particular 
molecule of gas would be on a certain hypothesis regarding 
the constitution of this class of bodies, Clausius and Max¬ 
well were yet able, by the application of the doctrine of 
probabilities, to predict that in the long run such and such 
a proportion of the molecules would, under given circum¬ 
stances, acquire such and such velocities; that there would 
take place, every second, such and such a number of colli¬ 
sions, etc.; and from these propositions they were able to 
deduce certain properties of gases, especially in regard to 
their heat-relations. In like manner, Darwin, while unable 
to say what the operation of variation and natural selection 
in every individual case will be, demonstrates that in the 
long run they will adapt animals to their circumstances. 
Whether or not existing animal forms are due to such ac¬ 
tion, or what position the theory ought to take, forms the 
subject of a discussion in which questions of fact and 
questions of logic are curiously interlaced. 


ii 

The object of reasoning is to find out, from the considera¬ 
tion of what we already know, something else which we do 


THE FIXATION OF BELIEF n 

not know. Consequently, reasoning is good if it be such 
as to give a true conclusion from true premises, and not 
otherwise. Thus, the question of validity is purely one of 
fact and not of thinking. A being the premises and B being 
the conclusion, the question is, whether these facts ar? 
really so related that if A is B is. If so, the inference is 
valid; if not, not. It is not in the least the question 
whether, when the premises are accepted by the mind, we 
feel an impulse to accept the conclusion also. It is true 
that we do generally reason correctly by nature. But that 
is an accident; the true conclusion would remain true if we 
had no impulse to accept it; and the false one would remain 
false, though we could not resist the tendency to believe 
in it. 

We are, doubtless, in the main logical animals, but we 
are not perfectly so. Most of us, for example, are natur¬ 
ally more sanguine and hopeful than logic would justify. 
We seem to be so constituted that in the absence of any 
facts to go upon we are happy and self-satisfied; so that the 
effect of experience is continually to counteract our hopes 
and aspirations. Yet a lifetime of the application of this 
corrective does not usually eradicate our sanguine disposi¬ 
tion. Where hope is unchecked by any experience, it is 
likely that our optimism is extravagant. Logicality in re¬ 
gard to practical matters is the most useful quality an ani¬ 
mal can possess, and might, therefore, result from the 
action of natural selection; but outside of these it is prob¬ 
ably of more advantage to the animal to have his mind 
filled with pleasing and encouraging visions, independently 
of their truth; and thus, upon unpractical subjects, natural 


12 


CHANCE AND LOGIC 


selection might occasion a fallacious tendency of thought. 

That which determines us, from given premises, to draw 
one inference rather than another, is some habit of mind, 
whether it be constitutional or acquired. The habit is good 
or otherwise, according as it produces true conclusions from 
true premises or not; and an inference is regarded as valid 
or not, without reference to the truth or falsity of its con¬ 
clusion specially, but according as the habit which deter¬ 
mines it is such as to produce true conclusions in general 
or not. The particular habit of mind which governs this 
or that inference may be formulated in a proposition whose 
truth depends on the validity of the inferences which the 
habit determines; and such a formula is called a guiding 
principle of inference. Suppose, for example, that we ob¬ 
serve that a rotating disk of copper quickly comes to rest 
when placed between the poles of a magnet, and we infer 
that this will happen with every disk of copper. The guid¬ 
ing principle is, that what is true of one piece of copper is 
true of another. Such a guiding principle with regard to 
copper would be much safer than with regard to many other 
substances — brass, for example. 

A book might be written to signalize all the most im¬ 
portant of these guiding principles of reasoning. It would 
probably be, we must confess, of no service to a person 
whose thought is directed wholly to practical subjects, and 
whose activity moves along thoroughly beaten paths. The 
problems which present themselves to such a mind are 
matters of routine which he has learned once for all to 
handle in learning his business. But let a man venture into 
an unfamiliar field, or where his results are not continually 


THE FIXATION OF BELIEF 


13 


checked by experience, and all history shows that the most 
masculine intellect will ofttimes lose his orientation and 
waste his efforts in directions which bring him no nearer to 
his goal, or even carry him entirely astray. He is like a 
ship on the open sea, with no one on board who understands 
the rules of navigation. And in such a case some general 
study of the guiding principles of reasoning would be sure 
to be found useful. 

The subject could hardly be treated, however, without 
being first limited; since almost any fact may serve as a 
guiding principle. But it so happens that there exists a 
division among facts, such that in one class are all those 
which are absolutely essential as guiding principles, while 
in the other are all those which have any other interest as 
objects of research. This division is between those which 
are necessarily taken for granted in asking whether a cer¬ 
tain conclusion follows from certain premises, and those 
which are not implied in that question. A moment’s thought 
will show that a variety of facts are already assumed when 
the logical question is first asked. It is implied, for in¬ 
stance, that there are such states of mind as doubt and 
belief — that a passage from one to the other is possible, 
the object of thought remaining the same, and that this 
transition is subject to some rules which all minds are alike 
bound by. As these are facts which we must already know 
before we can have any clear conception of reasoning at all, 
it cannot be supposed to be any longer of much interest to 
inquire into their truth or falsity. On the other hand, it 
is easy to believe that those rules of reasoning which are 
deduced from the very idea of the process are the ones 


i 4 CHANCE AND LOGIC 

which are the most essential; and, indeed, that so long as it 
conforms to these it will, at least, not lead to false conclu¬ 
sions from true premises. In point of fact, the importance 
of what may be deduced from the assumptions involved 
in the logical question turns out to be greater than might 
be supposed, and this for reasons which it is difficult to ex¬ 
hibit at the outset. The only one which I shall here men¬ 
tion is, that conceptions which are really products of logical 
reflections, without being readily seen to be so, mingle with 
our ordinary thoughts, and are frequently the causes of 
great confusion. This is the case, for example, with the 
conception of quality. A quality as such is never an object 
of observation. We can see that a thing is blue or green, 
but the quality of being blue and the quality of being green 
are not things which we see; they are products of logical 
reflections. The truth is, that common-sense, or thought 
as it first emerges above the level of the narrowly practical, 
is deeply imbued with that bad logical quality to which the 
epithet metaphysical is commonly applied; and nothing can 
clear it up but a severe course of logic. 

in 

We generally know when we wish to ask a question and 
when we wish to pronounce a judgment, for there is a dis¬ 
similarity between the sensation of doubting and that of 
believing. 

But this is not all which distinguishes doubt from belief. 
There is a practical difference. Our beliefs guide our de¬ 
sires and shape our actions. The Assassins, or followers 


THE FIXATION OF BELIEF 


1 5 


of the Old Man of the Mountain, used to rush into death at 
his least command, because they believed that obedience 
to him would insure everlasting felicity. Had they doubted 
this, they would not have acted as they did. So it is with 
every belief, according to its degree. The feeling of be* 
lieving is a more or less sure indication of there being estab¬ 
lished in our nature some habit which will determine our 
actions. Doubt never has such an effect. 

Nor must we overlook a third point of difference. Doubt 
is an uneasy and dissatisfied state from which we struggle 
to free ourselves and pass into the state of belief; while the 
latter is a calm and satisfactory state which we do not wish 
to avoid, or to change to a belief in anything else . 5 On 
the contrary, we cling tenaciously, not merely to believing, 
but to believing just what we do believe. 

Thus, both doubt and belief have positive effects upon us, 
though very different ones. Belief does not make us act at 
once, but puts us into such a condition that we shall behave 
in a certain way, when the occasion arises. Doubt has not 
the least effect of this sort, but stimulates us to action until 
it is destroyed. This reminds us of the irritation of a nerve 
and the reflex action produced thereby; while for the ana¬ 
logue of belief, in the nervous system, we must look to what 
are called nervous associations — for example, to that habit 
of the nerves in consequence of which the smell of a peach 
will make the mouth water. 


5 I am not speaking of secondary effects occasionally produced by the 
interference of other impulses. 


16 CHANCE AND LOGIC 

IV 

The irritation of doubt causes a struggle to attain a state 
of belief. I shall term this struggle inquiry, though it must 
be admitted that this is sometimes not a very apt 
designation. 

The irritation of doubt is the only immediate motive for 
the struggle to attain belief. It is certainly best for us 
that our beliefs should be such as may truly guide our 
actions so as to satisfy our desires; and this reflection will 
make us reject any belief which does not seem to have been 
so formed as to insure this result. But it will only do so 
by creating a doubt in the place of that belief. With the 
doubt, therefore, the struggle begins, and with the cessation 
of doubt it ends. Hence, the sole object of inquiry is the 
settlement of opinion. We may fancy that this is not 
enough for us, and that we seek not merely an opinion, 
but a true opinion. But put this fancy to the test, and it 
proves groundless; for as soon as a firm belief is reached 
we are entirely satisfied, whether the belief be false or true. 
And it is clear that nothing out of the sphere of our knowl¬ 
edge can be our object, for nothing which does not affect 
the mind can be a motive for a mental effort. The most 
that can be maintained is, that we seek for a belief that we 
shall think to be true. But we think each one of our be¬ 
liefs to be true, and, indeed, it is mere tautology to say so. 

That the settlement of opinion is the sole end of inquiry 
is a very important proposition. It sweeps away, at once, 
various vague and erroneous conceptions of proof. A few 
of these may be noticed here. 


THE FIXATION OF BELIEF 


*7 


1. Some philosophers have imagined that to start an in¬ 
quiry it was only necessary to utter or question or set it 
down on paper, and have even recommended us to begin 
our studies with questioning everything! But the mere 
putting of a proposition into the interrogative form does 
not stimulate the mind to any struggle after belief. There 
must be a real and living doubt, and without all this dis¬ 
cussion is idle. 

2. It is a very common idea that a demonstration must 
rest on some ultimate and absolutely indubitable proposi¬ 
tions. These, according to one school, are first principles 
of a general nature; according to another, are first sensa¬ 
tions. But, in point of fact, an inquiry, to have that com¬ 
pletely satisfactory result called demonstration, has only 
to start with propositions perfectly free from all actual 
doubt. If the premises are not in fact doubted at all, they 
cannot be more satisfactory than they are. 

3. Some people seem to love to argue a point after all 
the world is fully convinced of it. But no further advance 
can be made. When doubt ceases, mental action on the 
subject comes to an end; and, if it did go on, it would be 
without a purpose. 


v 

If the settlement of opinion is the sole object of inquiry, 
and if belief is of the nature of a habit, why should we not 
attain the desired end, by taking any answer to a question, 
which we may fancy, and constantly reiterating it to our¬ 
selves, dwelling on all which may conduce to that belief, 


18 


CHANCE AND LOGIC 


and learning to turn with contempt and hatred from any¬ 
thing which might disturb it? This simple and direct 
method is really pursued by many men. I remember once 
being entreated not to read a certain newspaper lest it might 
change my opinion upon free-trade. “ Lest I might be en¬ 
trapped by its fallacies and misstatements/’ was the form of 
expression. “ You are not/’ my friend said, “ a special 
student of political economy. You might, therefore, easily 
be deceived by fallacious arguments upon the subject. You 
might, then, if you read this paper, be led to believe in 
protection. But you admit that free-trade is the true doc¬ 
trine; and you do not wish to believe what is not true.” 
I have often known this system to be deliberately adopted. 
Still oftener, the instinctive dislike of an undecided state 
of mind, exaggerated into a vague dread of doubt, makes 
men cling spasmodically to the views they already take. 
The man feels that, if he only holds to his belief without 
wavering, it will be entirely satisfactory. Nor can it be 
denied that a steady and immovable faith yields great peace 
of mind. It may, indeed, give rise to inconveniences, as if 
a man should resolutely continue to believe that fire would 
not burn him, or that he would be eternally damned if he 
received his ingesta otherwise than through a stomach- 
pump. But then the man who adopts this method will not 
allow’ that its inconveniences are greater than its advantages. 
He will say, “ I hold steadfastly to the truth and the truth 
is always wholesome.” And in many cases it may very 
well be that the pleasure he derives from his calm faith 
overbalances any inconveniences resulting from its decep¬ 
tive character. Thus, if it be true that death is annihila- 


THE FIXATION OF BELIEF 


*9 


tion, then the man who believes that he will certainly go 
straight to heaven when he dies, provided he have fulfilled 
certain simple observances in this life, has a cheap pleasure 
which will not be followed by the least disappointment. 

A similar consideration seems to have weight with many 
persons in religious topics, for we frequently hear it said, 

“ Oh, I could not believe so-and-so, because I should be 
wretched if I did.” When an ostrich buries its head in the 
sand as danger approaches, it very likely takes the happiest 
course. It hides the danger, and then calmly says there 
is no danger; and, if it feels perfectly sure there is none, 
why should it raise its head to see? A man may go through 
life, systematically keeping out of view all that might cause 
a change in his opinions, and if he only succeeds — basing 
his method, as he does, on two fundamental psychological 
laws — I do not see what can be said against his doing so. 

It would be an egotistical impertinence to object that his 
procedure is irrational, for that only amounts to saying 
that his method of settling belief is not ours. He does not 
propose to himself to be rational, and indeed, will often 
talk with scorn of man’s weak and illusive reason. So let 
him think as he pleases. 

But this method of fixing belief, which may be called 
the method of tenacity, will be unable to hold its ground ^ 
in practice. The social impulse is against it. The man 
who adopts it will find that other men think differently from 
him, and it will be apt to occur to him in some saner moment 
that their opinions are quite as good as his own, and this 
will shake his confidence in his belief. This conception, 
that another man’s thought or sentiment may be equivalent 


20 


CHANCE AND LOGIC 


to one’s own, is a distinctly new step, and a highly important 
one. It arises from an impulse too strong in man to be 
suppressed, without danger of destroying the human species. 
Unless we make ourselves hermits, we shall necessarily in¬ 
fluence each other’s opinions; so that the problem becomes 
how to fix belief, not in the individual merely, but in the 
community. 

Let the will of the state act, then, instead of that of the 
individual. Let an institution be created which shall have 
for its object to keep correct doctrines before the attention 
of the people, to reiterate them perpetually, and to teach 
them to the young; having at the same time power to pre¬ 
vent contrary doctrines from being taught, advocated, or 
expressed. Let all possible causes of a change of mind 
be removed from men’s apprehensions. Let them be kept 
ignorant, lest they should learn of some reason to think 
otherwise than they do. Let their passions be enlisted, so 
that they may regard private and unusual opinions with 
hatred and horror. Then, let all men who reject the estab¬ 
lished belief be terrified into silence. Let the people turn 
out and tar-and-feather such men, or let inquisitions be 
made into the manner of thinking of suspected persons, 
and, when they are found guilty of forbidden beliefs, let 
them be subjected to some signal punishment. When com¬ 
plete agreement could not otherwise be reached, a general 
massacre of all who have not thought in a certain way has 
proved a very effective means of settling opinion in a 
country. If the power to do this be wanting, let a list of 
opinions be drawn up, to which no man of the least inde¬ 
pendence of thought can assent, and let the faithful be re- 


THE FIXATION OF BELIEF 


21 


quired to accept all these propositions, in order to segregate 
them as radically as possible from the influence of the rest 
of the world. 

This method has, from the earliest times, been one of 
the chief means of upholding correct theological and politi¬ 
cal doctrines, and of preserving their universal or catholic 
character. In Rome, especially, it has been practiced from 
the days of Numa Pompilius to those of Pius Nonus. This 
is the most perfect example in history; but wherever there 
is a priesthood — and no religion has been without one — 
this method has been more or less made use of. Wherever 
there is aristocracy, or a guild, or any association of a class 
of men whose interests depend or are supposed to depend 
on certain propositions, there will be inevitably found some 
traces of this natural product of social feeling. Cruelties 
always accompany this system; and when it is consistently 
carried out, they become atrocities of the most horrible 
kind in the eyes of any rational man. Nor should this 
occasion surprise, for the officer of a society does not feel 
justified in surrendering the interests of that society for 
the sake of mercy, as he might his own private interests. 
It is natural, therefore, that sympathy and fellowship should 
thus produce a most ruthless power. 

In judging this method of fixing belief, which may be 
called the method of authority, we must in the first place, 
allow its immeasurable mental and moral superiority to 
the method of tenacity. Its success is proportionally 
greater; and in fact it has over and over again worked the 
most majestic results. The mere structures of stone which 
it has caused to be put together — in Siam, for example, 


22 


CHANCE AND LOGIC 


in Egypt, and in Europe — have many of them a sublimity 
hardly more than rivaled by the greatest works of Nature. 
And, except the geological epochs, there are no periods of 
time so vast as those which are measured by some of these 
organized faiths. If we scrutinize the matter closely, we 
shall find that there has not been one of their creeds which 
has remained always the same; yet the change is so slow 
as to be imperceptible during one person s life, so that in¬ 
dividual belief remains sensibly fixed. For the mass of 
mankind, then, there is perhaps no better method than this. 
If it is their highest impulse to be intellectual slaves, then 
slaves they ought to remain. 

But no institution can undertake to regulate opinions 
upon every subject. Only the most important ones can be 
attended to, and on the rest men’s minds must be left to 
the action of natural causes. This imperfection will be 
no source of weakness so long as men are in such a state 
of culture that one opinion does not influence another — 
that is, so long as they cannot put two and two together. 
But in the most priest-ridden states some individuals will 
be found who are raised above that condition. These men 
possess a wider sort of social feeling; they see that men in 
other countries and in other ages have held to very different 
doctrines from those which they themselves have been 
brought up to believe; and they cannot help seeing that it 
is the mere accident of their having been taught as they 
have, and of their having been surrounded with the manners 
and associations they have, that has caused them to believe 
as they do and not far differently. And their candor can¬ 
not resist the reflection that there is no reason to rate their 


THE FIXATION OF BELIEF 


23 


own views at a higher value than those of other nations 
and other centuries; and this gives rise to doubts in their 
minds. 

They will further perceive that such doubts as these 
must exist in their minds with reference to every belief 
which seems to be determined by the caprice either of 
themselves or of those who originated the popular opinions. 
The willful adherence to a belief, and the arbitrary forcing 
of it upon others, must, therefore, both be given up and a 
new method of settling opinions must be adopted, which 
shall not only produce an impulse to believe, but shall also 
decide what proposition it is which is to be believed. Let 
the action of natural preferences be unimpeded, then, and 
under their influence let men conversing together and re¬ 
garding matters in different lights, gradually develop beliefs 
in harmony with natural causes. This method resembles 
that by which conceptions of art have been brought to 
maturity. The most perfect example of it is to be found 
in the history of metaphysical philosophy. Systems of this 
sort have not usually rested upon observed facts, at least 
not in any great degree. They have been chiefly adopted 
because their fundamental propositions seemed “ agreeable 
to reason.” This is an apt expression; it does not mean 
that which agrees with experience, but that which we find 
ourselves inclined to believe. Plato, for example, finds it 
agreeable to reason that the distances of the celestial spheres 
from one another should be proportional to the different 
lengths of strings which produce harmonious chords. Many 
philosophers have been led to their main conclusions by 
considerations like this; but this is the lowest and least 


24 


CHANCE AND LOGIC 


developed form which the method takes, for it is clear that 
another man might find Kepler’s [earlier] theory, that the 
celestial spheres are proportional to the inscribed and cir¬ 
cumscribed spheres of the different regular solids, more 
agreeable to his reason. But the shock of opinions will soon 
lead men to rest on preferences of a far more universal 
nature. Take, for example, the doctrine that man only 
acts selfishly — that is, from the consideration that acting 
in one way will afford him more pleasure than acting in 
another. This rests on no fact in the world, but it has had 
a wide acceptance as being the only reasonable theory. 

This method is far more intellectual and respectable 
from the point of view of reason than either of the others 
which we have noticed. But its failure has been the most 
manifest. It makes of inquiry something similar to the 
development of taste; but taste, unfortunately, is always 
more or less a matter of fashion, and accordingly, meta¬ 
physicians have never come to any fixed agreement, but 
the pendulum has swung backward and forward between 
a more material and a more spiritual philosophy, from the 
earliest times to the latest. And so from this, which has 
been called the a priori method, we are driven, in Lord 
Bacon’s phrase, to a true induction. We have examined 
into this a priori method as something which promised to 
deliver our opinions from their accidental and capricious 
element. But development, while it is a process which 
eliminates the effect of some casual circumstances, only 
magnifies that of others. This method, therefore, does not 
differ in a very essential way from that of authority. The 
government may not have lifted its finger to influence my 



THE FIXATION OF BELIEF 


*5 


convictions; I may have been left outwardly quite free to 
choose, we will say, between monogamy and polygamy, 
and appealing to my conscience only, I may have concluded 
that the latter practice is in itself licentious. But when I 
come to see that the chief obstacle to the spread of Chris¬ 
tianity among a people of as high culture as the Hindoos 
has been a conviction of the immorality of our way of 
treating women, I cannot help seeing that, though govern¬ 
ments do not interfere, sentiments in their development 
will be very greatly determined by accidental causes. Now, 
there are some people, among whom I must suppose that 
my reader is to be found, who, when they see that any be¬ 
lief of theirs is determined by any circumstance extraneous 
to the facts, will from that moment not merely admit in 
words that that belief is doubtful, but will experience a real 
doubt of it, so that it ceases to be a belief. 

To satisfy our doubts, therefore, it is necessary that a 
method should be found by which our beliefs may be caused 
by nothing human, but by some external permanency — 
by something upon which our thinking has no effect. Some 
mystics imagine that they have such a method in a private 
inspiration from on high. But that is only a form of the 
method of tenacity, in which the conception of truth as 
something public is not yet developed. Our external per¬ 
manency would not be external, in our sense, if it was re¬ 
stricted in its influence to one individual. It must be some¬ 
thing which affects, or might affect, every man. And, 
though these affections are necessarily as various as are 
individual conditions, yet the method must be such that 
the ultimate conclusion of every man shall be the same. 


26 


CHANCE AND LOGIC 


Such is the method of science. Its fundamental hypothesis, 
restated in more familiar language, is this: There are real 
things, whose characters are entirely independent of our 
opinions about them; whose realities affect our senses ac¬ 
cording to regular laws, and, though our sensations are 
as different as our relations to the objects, yet, by taking 
advantage of the laws of perception, we can ascertain by 
reasoning how things really are, and any man, if he have suf¬ 
ficient experience and reason enough about it, will be led to 
the one true conclusion. The new conception here involved 
is that of reality. It may be asked how I know that there 
are any realities. If this hypothesis is the sole support of 
my method of inquiry, my method of inquiry must not be 
used to support my hypothesis. The reply is this: i. If 
investigation cannot be regarded as proving that there are 
real things, it at least does not lead to a contrary conclu¬ 
sion; but the method and the conception on which it is 
based remain ever in harmony. No doubts of the method, 
therefore, necessarily arise from its practice, as is the case 
with all the others. 2. The feeling which gives rise to any 
method of fixing belief is a dissatisfaction at two repugnant 
propositions. But here already is a vague concession that 
there is some one thing to which a proposition should con¬ 
form. Nobody, therefore, can really doubt that there are 
realities, or, if he did, doubt would not be a source of dis¬ 
satisfaction. The hypothesis, therefore, is one which every 
mind admits. So that the social impulse does not cause 
me to doubt it. 3. Everybody uses the scientific method 
about a great many things, and only ceases to use it when 
he does not know how to apply it. 4. Experience of the 


THE FIXATION OF BELIEF 


27 


method has not led me to doubt it, but, on the contrary, 
scientific investigation has had the most wonderful triumphs 
in the way of settling opinion. These afford the explana¬ 
tion of my not doubting the method or the hypothesis which 
it supposes; and not having any doubt, nor believing that 
anybody else whom I could influence has, it would be the 
merest babble for me to say more about it. If there be 
anybody with a living doubt upon the subject, let him 
consider it. 

To describe the method of scientific investigation is the 
object of this series of papers. At present I have only room 
to notice some points of contrast between it and other 
methods of fixing belief. 

This is the only one of the four methods which presents 
any distinction of a right and a wrong way. If I adopt the 
method of tenacity and shut myself out from all influences, 
whatever I think necessary to doing this is necessary accord¬ 
ing to that method. So with the method of authority: the 
state may try to put down heresy by means which, from a 
scientific point of view, seems very ill-calculated to ac¬ 
complish its purposes; but the only test on that method is 
what the state thinks, so that it cannot pursue the method 
wrongly. So with the a priori method. The very essence of 
it is to think as one is inclined to think. All metaphysicians 
will be sure to do that, however they may be inclined to 
judge each other to be perversely wrong. The Hegelian 
system recognizes every natural tendency of thought as 
logical, although it is certain to be abolished by counter¬ 
tendencies. Hegel thinks there is a regular system in the 
succession of these tendencies, in consequence of which, 


28 


CHANCE AND LOGIC 


after drifting one way and the other for a long time, opinion 
will at last go right. And it is true that metaphysicians get 
the right ideas at last; Hegel’s system of Nature represents 
tolerably the science of that day; and one may be sure that 
whatever scientific investigation has put out of doubt will 
presently receive a priori demonstration on the part of the 
metaphysicians. But with the scientific method the case 
is different. I may start with known and observed facts 
to proceed to the unknown; and yet the rules which I follow 
in doing so may not be such as investigation would ap¬ 
prove. The test of whether I am truly following the 
method is not an immediate appeal to my feelings and pur¬ 
poses, but, on the contrary, itself involves the application 
of the method. Hence it is that bad reasoning as well as 
good reasoning is possible; and this fact is the foundation 
of the practical side of logic. 

It is not to be supposed that the first three methods of 
settling opinion present no advantage whatever over the 
scientific method. On the contrary, each has some peculiar 
convenience of its own. The a priori method is distin¬ 
guished for its comfortable conclusions. It is the nature 
of the process to adopt whatever belief we are inclined to, 
and there are certain flatteries to one’s vanities which we 
all believe by nature, until we are awakened from our pleas¬ 
ing dream by rough facts. The method of authority will 
always govern the mass of mankind; and those who wield 
the various forms of organized force in the state will never 
be convinced that dangerous reasoning ought not to be 
suppressed in some way. If liberty of speech is to be un¬ 
trammeled from the grosser forms of constraint, then uni- 


THE FIXATION OF BELIEF 


formity of opinion will be secured by a moral terrorism to 
which the respectability of society will give its thorough 
approval. Following the method of authority is the path 
of peace. Certain non-conformities are permitted; certain 
others (considered unsafe) are forbidden. These are dif¬ 
ferent in different countries and in different ages; but, 
wherever you are let it be known that you seriously hold 
a tabooed belief, and you may be perfectly sure of being 
treated with a cruelty no less brutal but more refined than 
hunting you like a wolf. Thus, the greatest intellectual 
benefactors of mankind have never dared, and dare not 
now, to utter the whole of their thought; and thus a shade 
of prima facie doubt is cast upon every proposition which 
is considered essential to the security of society. Singu¬ 
larly enough, the persecution does not all come from with¬ 
out; but a man torments himself and is oftentimes most 
distressed at finding himself believing propositions which 
he has been brought up to regard with aversion. The 
peaceful and sympathetic man will, therefore, find it hard 
to resist the temptation to submit his opinions to authority. 
But most of all I admire the method of tenacity for its 
strength, simplicity, and directness. Men who pursue it 
are distinguished for their decision of character, which be¬ 
comes very easy with such a mental rule. They do not 
waste time in trying to make up their minds to what they 
want, but, fastening like lightning upon whatever alterna¬ 
tive comes first, they hold to it to the end, whatever 
happens, without an instant’s irresolution. This is one of 
the splendid qualities which generally accompany brilliant, 
unlasting success. It is impossible not to envy the man who 


3° 


CHANCE AND LOGIC 


can dismiss reason, although we know how it must turn out 
at last. 

Such are the advantages which the other methods of 
settling opinions have over scientific investigation. A man 
should consider well of them; and then he should consider 
that, after all, he wishes his opinions to coincide with the 
fact, and that there is no reason why the results of these 
three methods should do so. To bring about this effect is the 
prerogative of the method of science. Upon such considera¬ 
tions he has to make his choice — a choice which is far 
more than the adoption of any intellectual opinion, which 
is one of the ruling decisions of his life, to which when once 
made he is bound to adhere. The force of habit will some¬ 
times cause a man to hold on to old beliefs, after he is in 
a condition to see that they have no sound basis. But re¬ 
flection upon the state of the case will overcome these 
habits, and he ought to allow reflection full weight. People 
sometimes shrink from doing this, having an idea that be¬ 
liefs are wholesome which they cannot help feeling rest on 
nothing. But let such persons suppose an analogous though 
different case from their own. Let them ask themselves 
what they would say to a reformed Mussulman who should 
hesitate to give up his old notions in regard to the relations 
of the sexes; or to a reformed Catholic who should still 
shrink from the Bible. Would they not say that these 
persons ought to consider the matter fully, and clearly 
understand the new doctrine, and then ought to embrace it 
in its entirety? But, above all, let it be considered that 
what is more wholesome than any particular belief, is in¬ 
tegrity of belief; and that to avoid looking into the support 


THE FIXATION OF BELIEF 


31 

of any belief from a fear that it may turn out rotten is 
quite as immoral as it is disadvantageous. The person who 
confesses that there is such a thing as truth, which is dis¬ 
tinguished from falsehood simply by this, that if acted on 
it will carry us to the point we aim at and not astray, and 
then though convinced of this, dares not know the truth 
and seeks to avoid it, is in a sorry state of mind, indeed. 

Yes, the other methods do have their merits: a clear 
logical conscience does cost something — just as any virtue, 
just as all that we cherish, costs us dear. But, we should 
not desire it to be otherwise. The genius of a man’s logical 
method should be loved and reverenced as his bride, whom 
he has chosen from all the world. He need not condemn 
the others; on the contrary, he may honor them deeply, 
and in doing so he only honors her the more. But she is 
the one that he has chosen, and he knows that he was right 
in making that choice. And having made it, he will work 
and fight for her, and will not complain that there are blows 
to take, hoping that there may be as many and as hard to 
give, and will strive to be the worthy knight and champion 
of her from the blaze of whose splendors he draws his 
inspiration and his courage. 


SECOND PAPER 


\ 


HOW TO MAKE OUR IDEAS CLEAR 1 

% 

I 

Whoever has looked into a modern treatise on logic of the 
common sort, will doubtless remember the two distinctions 
between clear and obscure conceptions, and between dis¬ 
tinct and conjused conceptions. They have lain in the 
books now for nigh two centuries, unimproved and un¬ 
modified, and are generally reckoned by logicians as among 
the gems of their doctrine. 

A clear idea is defined as one which is so apprehended 
that it will be recognized wherever it is met with, and so 
that no other will be mistaken for it. If it fails of this 
clearness, it is said to be obscure. 

This is rather a neat bit of philosophical terminology; 
yet, since it is clearness that they were defining, I wish the 
logicians had made their definition a little more plain. 
Never to fail to recognize an idea, and under no circum¬ 
stances to mistake another for it, let it come in how rec¬ 
ondite a form it may, would indeed imply such prodigious 
force and clearness of intellect as is seldom met with in this 
world. On the other hand, merely to have such an ac¬ 
quaintance with the idea as to have become familiar with it, 
and to have lost all hesitancy in recognizing it in ordinary 

1 Popular Science Monthly, January, 1878. 


32 


HOW TO MAKE OUR IDEAS CLEAR 


33 

cases, hardly seems to deserve the name of clearness of 
apprehension, since after all it only amounts to a subjective 
feeling of mastery which may be entirely mistaken. I take 
it, however, that when the logicians speak of “ clearness,” 
they mean nothing more than such a familiarity with an 
idea, since they regard the quality as but a small merit, 
which needs to be supplemented by another, which they call 
distinctness . 

A distinct idea is defined as one which contains nothing 
which is not clear. This is technical language; by the 
contents of an idea logicians understand whatever is con¬ 
tained in its definition. So that an idea is distinctly appre¬ 
hended, according to them, when we can give a precise 
definition of it, in abstract terms. Here the professional 
logicians leave the subject; and I would not have troubled 
the reader with what they have to say, if it were not such 
a striking example of how they have been slumbering 
through ages of intellectual activity, listlessly disregarding 
the enginery of modern thought, and never dreaming of 
applying its lessons to the improvement of logic. It is easy 
to show that the doctrine that familiar use and abstract 
distinctness make the perfection of apprehension, has its 
only true place in philosophies which have long been ex¬ 
tinct; and it is now time to formulate the method of attain¬ 
ing to a more perfect clearness of thought, such as we see 
and admire in the thinkers of our own time. 

When Descartes set about the reconstruction of philoso¬ 
phy, his first step was to (theoretically) permit skepticism 
and to discard the practice of the schoolmen of looking to 
authority as the ultimate source of truth. That done,, he 


34 


CHANCE AND LOGIC 


sought a more natural fountain of true principles, and pro¬ 
fessed to find it in the human mind; thus passing, in the 
directest way, from the method of authority to that of 
apriority, as described in my first paper. Self-conscious¬ 
ness was to furnish us with our fundamental truths, and to 
decide what was agreeable to reason. But since, evidently, 
not all ideas are true, he was led to note, as the first condi¬ 
tion of infallibility, that they must be clear. The distinc¬ 
tion between an idea seeming clear and really being so, 
never occurred to him. Trusting to introspection, as he 
did, even for a knowledge of external things, why should 
he question its testimony in respect to the contents of our 
own minds? But then, I suppose, seeing men, who seemed 
to be quite clear and positive, holding opposite opinions 
upon fundamental principles, he was further led to say that 
clearness of ideas is not sufficient, but that they need also 
to be distinct, i.e., to have nothing unclear about them. 
What he probably meant by this (for he did not explain 
himself with precision) was, that they must sustain the test 
of dialectical examination; that they must not only seem 
clear at the outset, but that discussion must never be able 
to bring to light points of obscurity connected with them. 

Such was the distinction of Descartes, and one sees that 
it was precisely on the level of his philosophy. It was 
somewhat developed by Leibnitz. This great and singular 
genius was as remarkable for what he failed to see as for 
what he saw. That a piece of mechanism could not do 
work perpetually without being fed with power in some 
form, was a thing perfectly apparent to him; yet he did not 
understand that the machinery of the mind can only trans- 


HOW TO MAKE OUR IDEAS CLEAR 


3$ 


form knowledge, but never originate it, unless it be fed 
with facts of observation. He thus missed the most essen¬ 
tial point of the Cartesian philosophy, which is, that to 
accept propositions which seem perfectly evident to us is 
a thing which, whether it be logical or illogical, we cannot 
help doing. Instead of regarding the matter in this way, 
he sought to reduce the first principles of science to formulas 
which cannot be denied without self-contradiction, and was 
apparently unaware of the great difference between his 
position and that of Descartes. So he reverted to the old 
formalities of logic, and, above all, abstract definitions 
played a great part in his philosophy. It was quite natural, 
therefore, that on observing that the method of Descartes 
labored under the difficulty that we may seem to ourselves 
to have clear apprehensions of ideas which in truth are 
very hazy, no better remedy occurred to him than to re¬ 
quire an abstract definition of every important term. Ac¬ 
cordingly, in adopting the distinction of clear and distinct 
notions, he described the latter quality as the clear appre¬ 
hension of everything contained in the definition; and the 
books have ever since copied his words. There is no danger 
that his chimerical scheme will ever again be over-valued. 
Nothing new can ever be learned by analyzing definitions. 
Nevertheless, our existing beliefs can be set in order by this 
process, and order is an essential element of intellectual 
economy, as of every other. It may be acknowledged, 
therefore, that the books are right in making familiarity 
with a notion the first step toward clearness of apprehen¬ 
sion, and the defining of it the second. But in omitting 
all mention of any higher perspicuity of thought, they 


36 


CHANCE AND LOGIC 


simply mirror a philosophy which was exploded a hundred 
years ago. That much-admired “ ornament of logic ” — 
the doctrine of clearness and distinctness — may be pretty 
enough, but it is high time to relegate to our cabinet of 
curiosities the antique bijou , and to wear about us some¬ 
thing better adapted to modern uses. 

The very first lesson that we have a right to demand 
that logic shall teach us is, how to make our ideas clear; 
and a most important one it is, depreciated only by minds 
who stand in need of it. To know what we think, to be 
masters of our own meaning, will make a solid foundation 
for great and weighty thought. It is most easily learned 
by those whose ideas are meagre and restricted; and far 
happier they than such as wallow helplessly in a rich mud 
of conceptions. A nation, it is true, may, in the course of 
generations, overcome the disadvantage of an excessive 
wealth of language and its natural concomitant, a vast, 
unfathomable deep of ideas. We may see it in history, 
slowly perfecting its literary forms, sloughing at length its 
metaphysics, and, by virtue of the untirable patience which 
is often a compensation, attaining great excellence in every 
branch of mental acquirement. The page of history is not 
yet unrolled which is to tell us whether such a people will 
or will not in the long run prevail over one whose ideas 
(like the words of their language) are few, but which pos¬ 
sesses a wonderful mastery over those which it has. For 
an individual, however, there can be no question that a 
few clear ideas are worth more than many confused ones. 
A young man would hardly be persuaded to sacrifice the 
greater part of his thoughts to save the rest; and the 



HOW TO MAKE OUR IDEAS CLEAR 37 

muddled head is the lea^t apt to see the necessity of such 
a sacrifice. Him we can usually only commiserate, as a 
person with a congenital defect. Time will help him, but 
intellectual maturity with regard to clearness comes rather 
late, an unfortunate arrangement of Nature, inasmuch as 
clearness is of less use to a man settled in life, whose errors 
have in great measure had their effect, than it would be 
to one whose path lies before him. It is terrible to see how 
a single unclear idea, a single formula without meaning, 
lurking in a young man’s head, will sometimes act like an 
obstruction of inert matter in an artery, hindering the nu¬ 
trition of the brain, and condemning its victim to pine away 
in the fullness of his intellectual vigor and in the midst of 
intellectual plenty. Many a man has cherished for years 
as his hobby some vague shadow of an idea, too meaning¬ 
less to be positively false; he has, nevertheless, passionately 
loved it, has made it his companion by day and by night, 
and has given to it his strength and his life, leaving all other 
occupations for its sake, and in short has lived with it and 
for it, until it has become, as it were, flesh of his flesh and 
bone of his bone; and then he has waked up some bright 
morning to find it gone, clean vanished away like the beauti¬ 
ful Melusina of the fable, and the essence of his life gone 
with it. I have myself known such a man; and who can 
tell how many histories of circle-squarers, metaphysicians, 
astrologers, and what not, may not be told in the old German 
story? 



3» 


CHANCE AND LOGIC 


II 

The principles set forth in the first of these papers lead, 
at once, to a method of reaching a clearness of thought of 
a far higher grade than the “ distinctness ” of the logicians. 
We have there found that the action of thought is excited 
by the irritation of doubt, and ceases when belief is at¬ 
tained; so that the production of belief is the sole function 
of thought. All these words, however, are too strong for 
my purpose. It is as if I had described the phenomena 
as they appear under a mental microscope. Doubt and 
Belief, as the words are commonly employed, relate to 
religious or other grave discussions. But here I use them 
to designate the starting of any question, no matter how 
small or how great, and the resolution of it. If, for in¬ 
stance, in a horse-car, I pull out my purse and find a five- 
cent nickel and five coppers, I decide, while my hand is 
going to the purse, in which way I will pay my fare. To 
call such a question Doubt, and my decision Belief, is cer¬ 
tainly to use words very disproportionate to the occasion. 
To speak of such a doubt as causing an irritation which 
needs to be appeased, suggests a temper which is uncom¬ 
fortable to the verge of insanity. Yet, looking at the matter 
minutely, it must be admitted that, if there is the least 
hesitation as to whether I shall pay the five coppers or the 
nickel (as there will be sure to be, unless I act from some 
previously contracted habit in the matter), though irritation 
is too strong a word, yet I am excited to such small mental 
activity as may be necessary to deciding how I shall act. 
Most frequently doubts arise from some indecision, however 


HOW TO MAKE OUR IDEAS CLEAR 


39 


momentary, in our action. Sometimes it is not so. I have, 
for example, to wait in a railway-station, and to pass the 
time I read the advertisements on the walls, I compare the 
advantages of different trains and different routes which 
I never expect to take, merely fancying myself to be in a 
state of hesitancy, because I am bored with having nothing 
to trouble me. Feigned hesitancy, whether feigned for 
mere amusement or with a lofty purpose, plays a great part 
in the production of scientific inquiry. However the doubt 
may originate, it stimulates the mind to an activity which 
may be slight or energetic, calm or turbulent. Images pass 
rapidly through consciousness, one incessantly melting into 
another, until at last, when all is over — it may be in a 
fraction of a second, in an hour, or after long years — w-e 
find ourselves decided as to how we should act under such 
circumstances as those which occasioned our hesitation. 
In other words, we have attained belief. 

In this process we observe two sorts of elements of con¬ 
sciousness, the distinction between which may best be made 
clear by means of an illustration. In a piece of music 
there are the separate notes, and there is the air. A single 
tone may be prolonged for an hour or a day, and it exists 
as perfectly in each second of that time as in the whole 
taken together; so that, as long as it is sounding, it might 
be present to a sense from which everything in the past was 
as completely absent as the future itself. But it is different 
with the air, the performance of which occupies a certain 
time, during the portions of which only portions of it are 
played. It consists in an orderliness in the succession of 
sounds which strike the ear at different times; and to per- 


40 


CHANCE AND LOGIC 


ceive it there must be some continuity of consciousness 
which makes the events of a lapse of time present to us. 
We certainly only perceive the air by hearing the separate 
notes; yet we cannot be said to directly hear it, for we hear 
only what is present at the instant, and an orderliness of 
succession cannot exist in an instant. These two sorts of 
objects, what we are immediately conscious of and what 
we are mediately conscious of, are found in all conscious¬ 
ness. Some elements (the sensations) are completely pres¬ 
ent at every instant so long as they last, while others (like 
thought) are actions having beginning, middle, and end, 
and consist in a congruence in the succession of sensations 
which flow through the mind. They cannot be immediately 
present to us, but must cover some portion of the past or 
future. Thought is a thread of melody running through 
the succession of our sensations. 

We may add that just as a piece of music may be written 
in parts, each part having its own air, so various systems 
of relationship of succession subsist together between the 
same sensations. These different systems are distinguished 
by having different motives, ideas, or functions. Thought 
is only one such system; for its sole motive, idea, and func¬ 
tion is to produce belief, and whatever does not concern 
that purpose belongs to some other system of relations. 
The action of thinking may incidentally have other results. 
It may serve to amuse us, for example, and among dilettanti 
it is not rare to find those who have so perverted thought 
to the purposes of pleasure that it seems to vex them to 
think that the questions upon which they delight to exercise 
it may ever get finally settled; and a positive discovery 


HOW TO MAKE OUR IDEAS CLEAR 


4i 


which takes a favorite subject out of the arena of literary 
debate is met with ill-concealed dislike. This disposition 
is the very debauchery of thought. But the soul and mean¬ 
ing of thought, abstracted from the other elements which 

accompany it, though it may be voluntarily thwarted, can 

— » 

never be made to direct itself tow T ard anything but the pro¬ 
duction of belief. Thought in action has for its only pos¬ 
sible motive the attainment of thought at rest; and whatever 
does not refer to belief is no part of the thought itself. 

And what, then, is belief? It is the demi-cadence which 
closes a musical phrase in the symphony of our intellectual 
life. We have seen that it has just three properties: First, 
it is something that we are aware of; second, it appeases 
the irritation of doubt; and, third, it involves the establish¬ 
ment in our nature of a rule of action, or, say for short, a 
habit. As it appeases the irritation of doubt, which is the 
motive for thinking, thought relaxes, and comes to rest for 
a moment when belief is reached. But, since belief is a 

4 --— , , t - - r - 

rule for action, the application of which involves further 
doubt and further thought, at the same time that it is a 
stopping-place, it is also a new starting-place for thought. 
That is why I have permitted myself to call it thought at 
rest, although thought is essentially an action. The final 
upshot of thinking is the exercise of volition, and of this 
thought no longer forms a part; but belief is only a stadium 
of mental action, an effect upon our nature due to thought, 
which will influence future thinking. 

The essence of belief is the establishment of a habit, 
and different beliefs are distinguished by the different modes 
of action to which they give rise. If beliefs do not differ 


42 


CHANCE AND LOGIC 


in this respect, if they appease the same doubt by producing 
the same rule of action, then no mere differences in the 
manner of consciousness of them can make them different 
beliefs, any more than playing a tune in different keys is 
playing different tunes. Imaginary distinctions are often 
drawn between beliefs which differ only in their mode of 
expression; — the wrangling which ensues is real enough, 
however. To believe that any objects are arranged as in 
Fig. i , and to believe that they are arranged as in Fig. 2, are 



Fig. 1 Fig. 2 

one and the same belief; yet it is conceivable that a man 
should assert one proposition and deny the other. Such 
false distinctions do as much harm as the confusion of be¬ 
liefs really different, and are among the pitfalls of which we 
ought constantly to beware, especially when we are upon 
metaphysical ground. One singular deception of this sort, 
which often occurs, is to mistake the sensation produced 
by our own unclearness of thought for a character of the 
object we are thinking. Instead of perceiving that the 
obscurity is purely subjective, we fancy that we contem- 





















HOW TO MAKE OUR IDEAS CLEAR 


43 


plate a quality of the object which is essentially mysterious; 
and if our conception be afterward presented to us in a 
clear form we do not recognize it as the same, owing to 
the absence of the feeling of unintelligibility. So long as 
this deception lasts, it obviously puts an impassable barrier 
in the way of perspicuous thinking; so that it equally in¬ 
terests the opponents of rational thought to perpetuate it, 
and its adherents to guard against it. 

Another such deception is to mistake a mere difference 
in the grammatical construction of two words for a dis¬ 
tinction between the ideas they express. In this pedantic 
age, when the general mob of writers attend so much more 
to words than to things, this error is common enough. When 
I just said that thought is an action, and that it consists 
in a relation, although a person performs an action but not 
a relation, which can only be the result of an action, yet 
there was no inconsistency in what I said, but only a gram¬ 
matical vagueness. 

From all these sophisms we shall be perfectly safe so long 
as we reflect that the whole function of thought is to pro¬ 
duce habits of action; and that whatever there is connected 
with a thought, but irrelevant to its purpose, is an accre- 
tion to it, but no part of it. If there be a unity among our 
sensations which has no reference to how we shall act on 
a given occasion, as when we listen to a piece of music, 
why we do not call that thinking. To develop its meaning, 
we have, therefore, simply to determine what habits it pro¬ 
duces, for what a thing means is simply what habits it in¬ 
volves. Now, the identity of a habit depends on how it 
might lead us to act, not merely under such circumstances 

f 


44 


CHANCE AND LOGIC 


as are likely to arise, but under such as might possibly 
occur, no matter how improbable they may be. What the 
habit is depends on when and how it causes us to act. As 
for the when, every stimulus to action is derived from per¬ 
ception; as for the how, every purpose of action is to pro¬ 
duce some sensible result. Thus, we come down to what is 
tangible and practical, as the root of every real distinction 
of thought, no matter how subtile it may be; and there is 
no distinction of meaning so fine as to consist in anything 
but a possible difference of practice. 

To see what this principle leads to, consider in the light 
of it such a doctrine as that of transubstantiation. The 
Protestant churches generally hold that the elements of the 
sacrament are flesh and blood only in a tropical sense; they 
nourish our souls as meat and the juice of it would our 
bodies. But the Catholics maintain that they are literally 
just that; although they possess all the sensible qualities of 
wafer-cakes and diluted wine. But we can have no con¬ 
ception of wine except what may enter into a belief, 
either — 

1. That this, that, or the other, is wine; or, 

2. That wine possesses certain properties. 

Such beliefs are nothing but self-notifications that we 
should, upon occasion, act in regard to such things as we 
believe to be wine according to the qualities which we be¬ 
lieve wine to possess. The occasion of such action would 
be some sensible perception, the motive of it to produce 
some sensible result. Thus our action has exclusive refer¬ 
ence to what affects the senses, our habit has the same bear¬ 
ing as our action, our belief the same as our habit, our 


HOW TO MAKE OUR IDEAS CLEAR 


45 


conception the same as our belief; and we can consequently 
mean nothing by wine but what has certain effects, direct 
or indirect, upon our senses; and to talk of something as 
having all the sensible characters of wine, yet being in 
reality blood, is senseless jargon. Now, it is not my object 
to pursue the theological question; and having used it as 
a logical example I drop it, without caring to anticipate 
the theologian’s reply. I only desire to point out how im¬ 
possible it is that we should have an idea in our minds 
which relates to anything but conceived sensible effects of 
things. Our idea of anything is our idea of its sensible 
effects; and if we fancy that we have any other we deceive 
ourselves, and mistake a mere sensation accompanying the 
thought for a part of the thought itself. It is absurd to say 
that thought has any meaning unrelated to its only func¬ 
tion. It is foolish for Catholics and Protestants to fancy 
themselves in disagreement about the elements of the sacra¬ 
ment, if they agree in regard to all their sensible effects, 
here or hereafter. 

. 1 -> 

It appears, then, that the rule for attaining the third 
grade of clearness of apprehension is as follows: Consider 
what effects, which might conceivably have practical bear- 
ings, we conceive the object of our conception to have. 
Then, our conception of these effects is the whole of our 
conception of the object. 

hi 

Let us illustrate this rule by some examples; and, to 
begin with the simplest one possible, let us ask what we 
mean by calling a thing hard. Evidently that it will not 


46 


CHANCE AND LOGIC 


be scratched by many other substances. The whole con¬ 
ception of this quality, as of every other, lies in its con¬ 
ceived effects. There is absolutely no difference between 
a hard thing and a soft thing so long as they are not brought 
to the test. Suppose, then, that a diamond could be crys¬ 
tallized in the midst of a cushion of soft cotton, and should 
remain there until it was finally burned up. Would it be 
false to say that that diamond was soft? This seems a 
foolish question, and would be so, in fact, except in the 
realm of logic. There such questions are often of the 
greatest utility as serving to bring logical principles into 
sharper relief than real discussions ever could. In study¬ 
ing logic we must not put them aside with hasty answers, 
but must consider them with attentive care, in order to 
make out the principles involved. We may, in the present 
case, modify our question, and ask what prevents us from 
saying that all hard bodies remain perfectly soft until they 
are touched, when their hardness increases with the pressure 
until they are scratched. Reflection will show that the 
reply is this: there would be no falsity in such modes of 
speech. They would involve a modification of our present 
usage of speech with regard to the words hard and soft, 
but not of their meanings. For they represent no fact to 
be different from what it is; only they involve arrange¬ 
ments of facts which would be exceedingly maladroit. This 
leads us to remark that the question of what would occur 
under circumstances which do not actually arise is not a 


✓ 

question of fact, but only of the most perspicuous arrange- 
| ment of them. For example, the question of free-will and 
\ fate in its simplest form, stripped of verbiage, is something 

V ~~ 


HOW TO MAKE OUR IDEAS CLEAR 


47 


like this: I have done something of which I am ashamed; 
could I, by an effort of the will, have resisted the tempta¬ 
tion, and done otherwise? The philosophical reply is, that 
this is not a question of fact, but only of the arrangement 
of facts. Arranging them so as to exhibit what is par¬ 
ticularly pertinent to my question — namely, that I ought 
to blame myself for having done wrong — it is perfectly 
true to say that, if I had willed to do otherwise than I did, 
I should have done otherwise. On the other hand, arrang¬ 
ing the facts so as to exhibit another important considera¬ 
tion, it is equally true that, when a temptation has once 
been allowed to work, it will, if it has a certain force, pro¬ 
duce its effect, let me struggle how I may. There is no 
objection to a contradiction in what would result from a 
false supposition. The reductio ad absurdum consists in 
showing that contradictory results would follow from a 
hypothesis which is consequently judged to be false. Many 
questions are involved in the free-will discussion, and I am 
far from desiring to say that both sides are equally right. 
On the contrary, I am of opinion that one side denies im¬ 
portant facts, and that the other does not. But what I do 
say is, that the above single question was the origin of the 
whole doubt; that, had it not been for this question, the 
controversy would never have arisen; and that this question 
is perfectly solved in the manner which I have indicated. 

Let us next seek a clear idea of Weight. This is another 

>*w~ 

very easy case. To say that a body is heavy means simply 
that, in the absence of opposing force, it will fall. This 
(neglecting certain specifications of how it will fall, etc., 
which exist in the mind of the physicist who uses the word) 


48 


CHANCE AND LOGIC 


is evidently the whole conception of weight. It is a fair 
question whether some particular facts may not account 
for gravity; but what we mean by the force itself is com¬ 
pletely involved in its effects. 

This leads us to undertake an account of the idea of 
Force in general. This is the great conception which, 

i 

developed in the early part of the seventeenth century 
from the rude idea of a cause, and constantly improved 
upon since, has shown us how to explain all the changes 
of motion which bodies experience, and how to think about 
all physical phenomena; which has given birth to modern 
science, and changed the face of the globe; and which, 
aside from its more special uses, has played a principal 
part in directing the course of modern thought, and in 
furthering modern social development. It is, therefore, 
worth some pains to comprehend it. According to our 
rule, we must begin by asking what is the immediate use 
of thinking about force; and the answer is, that we thus 
account for changes of motion. If bodies were left to 
themselves, without the intervention of forces, every 
motion would continue unchanged both in velocity and in 
direction. Furthermore, change of motion never takes 
place abruptly; if its direction is changed, it is always 
through a curve without angles; if its velocity alters, it is 
by degrees. The gradual changes which are constantly 
taking place are conceived by geometers to be compounded 
together according to the rules of the parallelogram of 
forces. If the reader does not already know what this is, 
he will find it, I hope, to his advantage to endeavor to 
follow the following explanation; but if mathematics are 



HOW TO MAKE OUR IDEAS CLEAR 


49 


insupportable to him, pray let him skip three paragraphs 
rather than that we should part company here. 

A path is a line whose beginning and end are distin¬ 
guished. Two paths are considered to be equivalent, which, 
beginning at the same point, lead to the same point. Thus 
the two paths, ABODE and A F G H E (Fig. 3), are 
equivalent. Paths which do not begin at the same point are 
considered to be equivalent, provided that, on moving either 
of them without turning it, but keeping it always parallel to 
its original position, [so that] when its beginning coincides 
with that of the other path, the ends also coincide. Paths are 
considered as geometrically added together, when one be¬ 
gins where the other ends; thus the path A E is conceived to 
be a sum of A B, B C, C D, and D E. In the parallelogram 
of Fig. 4 the diagonal A C is the sum of A B and B C; 
or, since A D is geometrically equivalent to B C, A C is 
the geometrical sum of A B and A D. 


A - B 




All this is purely conventional. It simply amounts to 
this: that we choose to call paths having the relations I 
have described equal or added. But, though it is a con¬ 
vention, it is a convention with a good reason. The rule 
for geometrical addition may be applied not only to paths, 
but to any other things which can be represented by paths. 
Now, as a path is determined by the varying direction and 







50 


CHANCE AND LOGIC 


distance of the point which moves over it from the starting- 
point, it follows that anything which from its beginning to 
its end is determined by a varying direction and a varying 
magnitude is capable of being represented by a line. 
Accordingly, velocities may be represented by lines, for 
they have only directions and rates. The same thing is 
true of accelerations, or changes of velocities. This is 
evident enough in the case of velocities; and it becomes 
evident for accelerations if we consider that precisely what 
velocities are to positions — namely, states of change of 
them — that accelerations are to velocities. 

The so-called “ parallelogram of forces ” is simply a 
rule for compounding accelerations. The rule is, to 
represent the accelerations by paths, and then to geo¬ 
metrically add the paths. The geometers, however, not 
only use the “ parallelogram of forces ” to compound dif¬ 
ferent accelerations, but also to resolve one acceleration 
into a sum of several. Let A B (Fig. 5) be the path 

which represents a certain 
acceleration — say, such a 
change in the motion of a 
body that at the end of 
one second the body will, 
under the influence of that 
change, be in a position 
different from what it 
would have had if its motion had continued unchanged, such 
that a path equivalent to A B would lead from the latter 
position to the former. This acceleration may be considered 
as the sum of the accelerations represented by A C and C B. 



Fig. 5 




HOW TO MAKE OUR IDEAS CLEAR 51 

It may also be considered as the sum of the very different 
accelerations represented by A D and D B, where A D is 
almost the opposite of A C. And it is clear that there is 
an immense variety of ways in which A B might be resolved 
into the sum of two accelerations. 

After this tedious explanation, which I hope, in view of 
the extraordinary interest of the conception of force, may 
not have exhausted the reader’s patience, we are prepared 
at last to state the grand fact which this conception em¬ 
bodies. This fact is that if the actual changes of motion^ 
which the different particles of bodies experience are each 
resolved in its appropriate way, each component accelera¬ 
tion is precisely such as is prescribed by a certain law of 
Nature, according to which bodies in the relative positions 
which the bodies in question actually have at the moment, 2 
always receive certain accelerations, which, being com¬ 
pounded by geometrical addition, give the acceleration 
which the body actually experiences. 

This is the only fact which the idea of force represents, 
and whoever will take the trouble clearly to apprehend 
what this fact is, perfectly comprehends what force is. 
Whether we ought to say that a force is an acceleration, 
or that it causes an acceleration, is a mere question of pro¬ 
priety of language, which has no more to do with our real 
meaning than the difference between the French idiom “II 
fait froid ” and its English equivalent “ It is cold” Yet 
it is surprising to see how this simple affair has muddled 
men’s minds. In how many profound treatises is not force 
spoken of as a “ mysterious entity,” which seems to be 

2 Possibly the velocities also have to be taken into account. 


52 CHANCE AND LOGIC 

only a way of confessing that the author despairs of ever 
getting a clear notion of what the word means! In a re¬ 
cent admired work on Analytic Mechanics it is stated 
that we understand precisely the effect of force, but what 
force itself is we do not understand! This is simply a self- 
contradiction. The idea which the word force excites in 
our minds has no other function than to affect our actions, 
and these actions can have no reference to force otherwise 
than through its effects. Consequently, if we know what 
the effects of force are, we are acquainted with every fact 
which is implied in saying that a force exists, and there is 
nothing more to know. The truth is, there is some vague 
notion afloat that a question may mean something which the 
mind cannot conceive; and when some hair-splitting 
philosophers have been confronted with the absurdity of 
such a view, they have invented an empty distinction be¬ 
tween positive and negative conceptions, in the attempt to 
give their non-idea a form not obviously nonsensical. The 
nullity of it is sufficiently plain from the considerations 
given a few pages back; and, apart from those considera¬ 
tions, the quibbling character of the distinction must have 
struck every mind accustomed to real thinking. 

IV 

Let us now approach the subject of logic, and consider 
a conception which particularly concerns it, that of reality . 
Taking clearness in the sense of familiarity, no idea could 
be clearer than this. Every child uses it with perfect con¬ 
fidence, never dreaming that he does not understand it. 




HOW TO MAKE OUR IDEAS CLEAR 


53 


As for clearness in its second grade, however, it would 
probably puzzle most men, even among those of a reflective 
turn of mind, to give an abstract definition of the real. 
Yet such a definition may perhaps be reached by consider¬ 
ing the points of difference between reality and its opposite, 
fiction. A figment is a product of somebody’s imagination; 
it has such characters as his thought impresses upon it. 
That those characters are independent of how you or I 
think is an external reality. There are, however, phe¬ 
nomena within our own minds, dependent upon our thought, 
which are at the same time real in the sense that we really 
think them. But though their characters depend on how 
we think, they do not depend on what we think those char-^ 
acters to be. Thus, a dream has a real existence as a 
mental phenomenon, if somebody has really dreamt it; 
that he dreamt so and so, does not depend on what anybody 
thinks was dreamt, but is completely independent of all 
opinion on the subject. On the other hand, considering, 
not the fact of dreaming, but the thing dreamt, it retains 
its peculiarities by virtue of no other fact than that it was 
dreamt to possess them. Thus we may define the real as 
that whose characters are independent of what anybody ([ 
may think them to be. 

But, however satisfactory such a definition may be found, 
it would be a great mistake to suppose that it makes the 
idea of reality perfectly clear. Here, then, let us apply 
our rules. According to them, reality, like every other 
quality, consists in the peculiar sensible effects which things 
partaking of it produce. The only effect which real things 
have is to cause belief, for all the sensations which they 


54 


CHANCE AND LOGIC 


excite emerge into consciousness in the form of beliefs. 
The question, therefore, is, how is true belief (or belief in 
the real) distinguished from false belief (or belief in fic¬ 
tion). Now, as we have seen in the former paper, the 
ideas of truth and falsehood, in their full development, 
appertain exclusively to the scientific method of settling 
opinion. A person who arbitrarily chooses the propositions 
which he will adopt can use the word truth only to empha¬ 
size the expression of his determination to hold on to his 
choice. Of course, the method of tenacity never prevailed 
exclusively; reason is too natural to men for that. But in 
the literature of the dark ages we find some fine examples 
of it. When Scotus Erigena is commenting upon a poetical 
passage in which hellebore is spoken of as having caused 
the death of Socrates, he does not hesitate to inform the 
inquiring reader that Helleborus and Socrates were two 
eminent Greek philosophers, and that the latter having been 
overcome in argument by the former took the matter to 
heart and died of it! What sort of an idea of truth could 
a man have who could adopt and teach, without the quali¬ 
fication of a perhaps, an opinion taken so entirely at ran¬ 
dom? The real spirit of Socrates, who I hope would have 
been delighted to have been “ overcome in argument,” be¬ 
cause he would have learned something by it, is in curious 
contrast with the naive idea of the glossist, for whom dis¬ 
cussion would seem to have been simply a struggle. When 
philosophy began to awake from its long slumber, and 
before theology completely dominated it, the practice seems 
to have been for each professor to seize upon any philoso¬ 
phical position he found unoccupied and which seemed a 



HOW TO MAKE OUR IDEAS CLEAR 


55 


strong one, to intrench himself in it, and to sally forth from 
time to time to give battle to the others. Thus, even the 
scanty records we possess of those disputes enable us to 
make out a dozen or more opinions held by different teachers 
at one time concerning the question of nominalism and 
realism. Read the opening part of the Historia Calami - 
tatum of Abelard, who was certainly as philosophical as 
any of his contemporaries, and see the spirit of combat 
which it breathes. For him, the truth is simply his par¬ 
ticular stronghold. When the method of authority pre¬ 
vailed, the truth meant little more than the Catholic faith. \ 
All the efforts of the scholastic doctors are directed toward \ 
harmonizing their faith in Aristotle and their faith in the 
Church, and one may search their ponderous folios through 
without finding an argument which goes any further. It is 
noticeable that where different faiths flourish side by side, 
renegades are looked upon with contempt even by the party 
whose belief they adopt; so completely has the idea of 
loyalty replaced that of truth-seeking. Since the time of 
Descartes, the defect in the conception of truth has been 
less apparent. Still, it will sometimes strike a scientific 
man that the philosophers have been less intent on finding 
out what the facts are, than on inquiring what belief is 
most in harmony with their system. It is hard to convince 
a follower of the a priori method by adducing facts; but 
show him that an opinion he is defending is inconsistent 
with what he has laid down elsewhere, and he will be very 
apt to retract it. These minds do not seem to believe that 
disputation is ever to cease; they seem to think that the 
opinion which is natural for one man is not so for another, 


56 


CHANCE AND LOGIC 


and that belief will, consequently, never be settled. In 
contenting themselves with fixing their own opinions by a 
method which would lead another man to a different result, 
they betray their feeble hold of the conception of what 
truth is. 

On the other hand, all the followers of science are fully 
persuaded that the processes of investigation, if only pushed 
far enough, will give one certain solution to every question 
to which they can be applied. One man may investigate 
the velocity of light by studying the transits of Venus and 
the aberration of the stars; another by the oppositions of 
Mars and the eclipses of Jupiter’s satellites; a third by the 
method of Fizeau; a fourth by that of Foucault; a fifth 

4 

by the motions of the curves of Lissajoux; a sixth, a seventh, 
an eighth, and a ninth, may follow the different methods 
of comparing the measures of statical and dynamical elec¬ 
tricity. They may at first obtain different results, but, 
as each perfects his method and his processes, the results 
will move steadily together toward a destined center. So 
with all scientific research. Different minds may set out 
with the most antagonistic views, but the progress of in¬ 
vestigation carries them by a force outside of themselves 
to one and the same conclusion. This activity of thought 
by which we are carried, not where we wish, but to a fore¬ 
ordained goal, is like the operation of destiny. No modi¬ 
fication of the point of view taken, no selection of other 
facts for study, no natural bent of mind even, can enable 
a man to escape the predestinate opinion. This great law 
is embodied in the conception of truth and reality. The 







HOW TO MAKE OUR IDEAS CLEAR 


57 

opinion which is fated ’ to be ultimately agreed to by all 
who investigate, is what we mean by the truth, and the ob¬ 
ject represented in this opinion is the real. That is the way 
I would explain reality. 

But it may be said that this view is directly opposed 
to the abstract definition which we have given of reality, 
inasmuch as it makes the characters of the real depend 
on what is ultimately thought about them. But the answer 
to this is that, on the one hand, reality is independent, not 
necessarily of thought in general, but only of what you or 
I or any finite number of men may think about it; and that, 
on the other hand, though the object of the final opinion 
depends on What that opinion is, yet what that opinion is 
does not depend on what you or I or any man thinks. Our 
perversity and that of others may indefinitely postpone the 
settlement of opinion; it might even conceivably cause an 
arbitrary proposition to be universally accepted as long as 
the human race should last. Yet even that would not change 
the nature of the belief, which alone could be the result of 
investigation carried sufficiently far; and if, after the ex¬ 
tinction of our race, another should arise with faculties and 
disposition for investigation, that true opinion must be the 
one which they would ultimately come to. “ Truth crushed 
to earth shall rise again/’ and the opinion which would 
finally result from investigation does not depend on how 
anybody may actually think. But the reality of that which 
is real does depend on the real fact that investigation is 

3 Fate means merely that which is sure to come true, and can nohow 
be avoided. It is a superstition to suppose that a certain sort of events 
are ever fated, and it is another to suppose that the word fate can never 
be freed from its superstitious taint. We are all fated to die. 




CHANCE AND LOGIC 


destined to lead, at last, if continued long enough, to a 
belief in it. 

But I may be asked what I have to say to all the minute 
facts of history, forgotten never to be recovered, to the lost 
books of the ancients, to the buried secrets. 

“ Full many a gem of purest ray serene 

The dark, unfathomed caves of ocean bear; 

Full many a flower is born to blush unseen, 

And waste its sweetness on the desert air.” 

Do these things not really exist because they are hopelessly 
beyond the reach of our knowledge? And then, after the 
universe is dead (according to the prediction of some scien¬ 
tists), and all life has ceased forever, will not the shock 
of atoms continue though there will be no mind to know it? 
To this I reply that, though in no possible state of knowl¬ 
edge can any number be great enough to express the rela¬ 
tion between the amount of what rests unknown to the 
amount of the known, yet it is unphilosophical to suppose 
that, with regard to any given question (which has any 
clear meaning), investigation would not bring forth a solu¬ 
tion of it, if it were carried far enough. Who would have 
said, a few years ago, that we could ever know of what 
substances stars are made whose light may have been longer 
in reaching us than the human race has existed? Who can 
be sure of what we shall not know in a few hundred years? 
Who can guess what would be the result of continuing the 
pursuit of science for ten thousand years, with the activity 
of the last hundred? And if it were to go on for a million, 
or a billion, or any number of years you please, how is it 


HOW TO MAKE OUR IDEAS CLEAR 


59 


possible to say that there is any question which might not 
ultimately be solved? 

But it may be objected, “ Why make so much of these 
remote considerations, especially when it is your principle 
that only practical distinctions have a meaning? ” Well, 
I must confess that it makes very little difference whether 
we say that a stone on the bottom of the ocean, in complete 
darkness, is brilliant or not — that is to say, that it probably 
makes no difference, remembering always that that stone 
may be fished up to-morrow. But that there are gems at 
the bottom of the sea, flowers in the untraveled desert, etc., 
are propositions which, like that about a diamond being 
hard when it is not pressed, concern much more the arrange¬ 
ment of our language than they do the meaning of our ideas. 

It seems to me, however, that we have, by the application 
of our rule, reached so clear an apprehension of what we 
mean by reality, and of the fact which the idea rests on. 
that we should not, perhaps, be making a pretension so pre¬ 
sumptuous as it would be singular, if we were to offer a 
metaphysical theory of existence for universal acceptance 
among those who employ the scientific method of fixing be¬ 
lief. However, as metaphysics is a subject much more 
curious than useful, the knowledge of which, like that of a 
sunken reef, serves chiefly to enable us to keep clear of it, 
I will not trouble the reader with any more Ontology at 
this moment. I have already been led much further into 
that path than I should have desired; and I have given the 
reader such a dose of mathematics, psychology, and all 
that is most abstruse, that I fear he may already have left 
me, and that what I am now wTiting is for the compositor 



6o 


CHANCE AND LOGIC 


and proofreader exclusively. I trusted to the importance 
of the subject. There is no royal road to logic, and really 
valuable ideas can only be had # at the price of close atten¬ 
tion. But I know that in the matter of ideas the public 
prefer the cheap and nasty; and in my next paper I am 
going to return to the easily intelligible, and not wander 
from it again. The reader who has been at the pains of 
wading through this paper, shall be rewarded in the next 
one by seeing how beautifully what has been developed 
in this tedious way can be applied to the ascertainment of 
the rules of scientific reasoning. 

We have, hitherto, not crossed the threshold of scientific 

* 

logic. It is certainly important to know how to make our 
ideas clear, but they may be ever so clear without being 
true. How to make them so, we have next to study. How 
to give birth to those vital and procreative ideas which 
multiply into a thousand forms and diffuse themselves 
everywhere, advancing civilization and making the dignity 
of man, is an art not yet reduced to rules, but of the secret 
of which the history of science affords some hints. 





THIRD PAPER 


THE DOCTRINE OF CHANCES 1 

I 

- 

It is a common observation that a science first begins to be 
exact when it is quantitatively treated. What are called 
the exact sciences are no others than the mathematical ones. 
Chemists reasoned vaguely until Lavoisier showed them 
how to apply the balance to the verification of their theories, 
when chemistry leaped suddenly into the position of the 
most perfect of the classificatory sciences. It has thus 
become so precise and certain that we usually think of it 
along with optics, thermotics, and electrics. But these are 
studies of general laws, while chemistry considers merely 
the relations and classification of certain objects; and be¬ 
longs, in reality, in the same category as systematic botany 
and zoology. Compare it with these last, however, and 
the advantage that it derives from its quantitative treatment 
is very evident. 

The rudest numerical scales, such as that by which the 
mineralogists distinguish the different degrees of hardness, 
are found useful. The mere counting of pistils and sta¬ 
mens sufficed to bring botany out of total chaos into some 
kind of form. It is not, however, so much from counting 
as from measuring , not so much from the conception of 

1 Popular Science Monthly, March, 1878. 

61 





62 


CHANCE AND LOGIC 


number as from that of continuous quantity, that the advan¬ 
tage of mathematical treatment comes. Number, after all, 
only serves to pin us down to a precision in our thoughts 
which, however beneficial, can seldom lead to lofty concep¬ 
tions, and frequently descends to pettiness. Of those two 
faculties of which Bacon speaks, that which marks differ¬ 
ences and that which notes resemblances, the employment of 
number can only aid the lesser one; and the excessive use 
of it must tend to narrow the powers of the mind. But the 
conception of continuous quantity has a great office to ful¬ 
fill, independently of any attempt at precision. Far from 
tending to the exaggeration of differences, it is the direct 
instrument of the finest generalizations. When a naturalist 
wishes to study a species, he collects a considerable num¬ 
ber of specimens more or less similar. In contemplating 
them, he observes certain ones which are more or less alike 
in some particular respect. They all have, for instance, 
a certain S-shaped marking. He observes that they are 
not precisely alike, in this respect; the S has not precisely 
the same shape, but the differences are such as to lead him 
to believe that forms could be found intermediate between 
any two of those he possesses. He, now, finds other forms 
apparently quite dissimilar — say a marking in the form 
of a C — and the question is, whether he can find inter¬ 
mediate ones which will connect these latter with the others. 
This he often succeeds in doing in cases where it would at 
first be thought impossible; whereas; he sometimes finds 
those which differ, at first glance, much less, to be separated 
in Nature by the non-occurrence of intermediaries. In 
this way, he builds up from the study of Nature a new gen- 


THE DOCTRINE OF CHANCES 


6 3 

eral conception of the character in question. He obtains, 
for example, an idea of a leaf which includes every part 
of the flower, and an idea of a vertebra which includes the 
skull. I surely need not say much to show what a logical 
engine there is here. It is the essence of the method of the 
naturalist.- How he applies it first to one character, and 
then to another, and finally obtains a notion of a species 
of animals, the differences between whose members, however 
great, are confined within limits, is a matter which does not 
here concern us. The whole method of classification must 
be considered later; but, at present, I only desire to point 
out that it is by taking advantage of the idea of continuity, 
or the passage from one form to another by insensible de¬ 
grees, that the naturalist builds his conceptions. Now, the 
naturalists are the great builders of conceptions; there is 
no other branch of science where so much of this work is 
done as in theirs; and we must, in great measure, take them 
for our teachers in this important part of logic. And it will 
be found everywhere that the idea of continuity is a power¬ 
ful aid to the formation of true and fruitful conceptions. 
By means of it, the greatest differences are broken down 
and resolved into differences of degree, and the incessant 
application of it is of the greatest value in broadening our 
conceptions. I propose to make a great use of this idea in 
the present series of papers; and the particular series of 
important fallacies, which, arising from a neglect of it, have 
desolated philosophy, must further on be closely studied. 

2 [Later, pp. 170 ff. and 215 ff., it is shown that continuity is also at 
the basis of mathematical generalization. See also article on Synechism 
in Baldwin’s Dictionary of Philosophy, j 


64 


CHANCE AND LOGIC 


At present, I simply call the reader’s attention to the utility 
of this conception. 

In studies of numbers, the idea of continuity is so in¬ 
dispensable, that it is perpetually introduced even where 
there is no continuity in fact, as where we say that there 
are in the United States 10.7 inhabitants per square mile, or 
that in New York 14.72 persons live in the average house. 3 
Another example is that law of the distribution of errors 
which Quetelet, Galton, and others, have applied with so 
much success to the study of biological and social matters. 
This application of continuity to cases where it does not 
really exist illustrates, also, another point which will here¬ 
after demand a separate study, namely, the great utility 
which fictions sometimes have in science. 


11 

The theory of probabilities is simply the science of logic 
quantitatively treated. There are two conceivable cer¬ 
tainties with reference to any hypothesis, the certainty of 
its truth and the certainty of its falsity. The numbers one 
and zero are appropriated, in this calculus, to marking these 
extremes of knowledge; while fractions having values inter¬ 
mediate between them indicate, as we may vaguely say, the 
degrees in which the evidence leans toward one or the other. 
The general problem of probabilities is, from a given state 

3 This mode of thought is so familiarly associated with all exact nu¬ 
merical consideration, that the phrase appropriate to it is imitated by 
shallow writers in order to produce the appearance of exactitude where 
none exists. Certain newspapers which affect a learned tone talk of “ the 
average man,” when they simply mean most men , and have no idea of 
striking an average. 



THE DOCTRINE OF CHANCES 


6 5 

of facts, to determine the numerical probability of a pos¬ 
sible fact. This is the same as to inquire how much the 
given facts are worth, considered as evidence to prove the 
possible fact. Thus the problem of probabilities is simply 
the general problem of logic. 

Probability is a continuous quantity, so that great ad¬ 
vantages may be expected from this mode of studying logic. 
Some writers have gone so far as to maintain that, by means 
of the calculus of chances, every solid inference may be 
represented by legitimate arithmetical operations upon the 
numbers given in the premises. If this be, indeed, true, 
the great problem of logic, how it is that the observation 
of one fact can give us knowledge of another independent 
fact, is reduced to a mere question of arithmetic. It seems 
proper to examine this pretension before undertaking any 
more recondite solution of the paradox. 

But, unfortunately, writers on probabilities are not agreed 
in regard to this result. This branch of mathematics is the 
only one, I believe, in which good writers frequently get 
results entirely erroneous. In elementary geometry the 
reasoning is frequently fallacious, but erroneous conclusions 
are avoided; but it may be doubted if there is a single ex¬ 
tensive treatise on probabilities in existence which does not 
contain solutions absolutely indefensible. This is partly 
owing to the want of any regular method of procedure; for 
the subject involves too many subtilties to make it easy to 
put its problems into equations without such an aid. But, 
beyond this, the fundamental principles of its calculus are 
more or less in dispute. In regard to that class of questions 
to which it is chiefly applied for practical purposes, there 


66 


CHANCE AND LOGIC 


is comparatively little doubt; but in regard to others to 
which it has been sought to extend it, opinion is somewhat 
unsettled. 

This last class of difficulties can only be entirely over¬ 
come by making the idea of probability perfectly clear in 
our minds in the way set forth in our last paper. 

in 

To get a clear idea of what we mean by probability, we 
have to consider what real and sensible difference there is 
between one degree of probability and another. 

The character of probability belongs primarily, without 
doubt, to certain inferences. Locke explains it as follows: 
After remarking that the mathematician positively knows 
that the sum of the three angles of a triangle is equal to 
two right angles because he apprehends the geometrical 
proof, he thus continues: “ But another man who never took 
the pains to observe the demonstration, hearing a mathe¬ 
matician, a man of credit, affirm the three angles of a tri¬ 
angle to be equal to two right ones, assents to it; i.e., re¬ 
ceives it for true. In which case the foundation of his as¬ 
sent is the probability of the thing, the proof being such as, 
for the most part, carries truth with it; the man on whose 
testimony he receives it not being wont to affirm anything 
contrary to, or besides his knowledge, especially in matters 
of this kind.” The celebrated Essay concerning Human 
Understanding contains many passages which, like this 
one, make the first steps in profound analyses which are not 
further developed. It was shown in the first of these papers 


THE DOCTRINE OF CHANCES 


67 


that the validity of an inference does not depend on any 
tendency of the mind to accept it, however strong such ten¬ 
dency may be; but consists in the real fact that, when 
premises like those of the argument in question are true, 
conclusions related to them like that of this argument are 
also true. It was remarked that in a logical mind an argu¬ 
ment is always conceived as a member of a genus of 
arguments all constructed in the same way, and such that, 
when their premises are real facts, their conclusions are so 
also. If the argument is demonstrative, then this is always 
so; if it is only probable, then it is for the most part so. 
As Locke says, the probable argument is “ such as for the 
most part carries truth with it.” 

According to this, that real and sensible difference be¬ 
tween one degree of probability and another, in which the 
meaning of the distinction lies, is that in the frequent em¬ 
ployment of two different modes of inference, one will carry 
truth with it oftener than the other. It is evident that this 
is the only difference there is in the existing fact. Having 
certain premises, a man draws a certain conclusion, and as 
far as this inference alone is concerned the only possible 
practical question is whether that conclusion is true or not, 
and between existence and non-existence there is no middle 
term. “ Being only is and nothing is altogether not,” said 
Parmenides; and this is in strict accordance with the analy¬ 
sis of the conception of reality given in the last paper. For 
we found that the distinction of reality and fiction depends 
on the supposition that sufficient investigation would cause 
one opinion to be universally received and all others to be 
rejected. That presupposition, involved in the very con- 


68 


CHANCE AND LOGIC 


ceptions of reality and figment, involves a complete sunder¬ 
ing of the two. It is the heaven-and-hell idea in the do¬ 
main of thought. But, in the long run, there is a real fact 
which corresponds to the idea of probability, and it is that 
a given mode of inference sometimes proves successful and 
sometimes not, and that in a ratio ultimately fixed. As we 
go on drawing inference after inference of the given kind, 
during the first ten or hundred cases the ratio of successes 
may be expected to show considerable fluctuations; but 
when we come into the thousands and millions, these fluc¬ 
tuations become less and less; and if we continue long 
enough, the ratio will approximate toward a fixed limit. 
We may, therefore, define the probability of a mode of 
argument as the proportion of cases in which it carries truth 
with it. 

The inference from the premise, A, to the conclusion, B, 
depends, as we have seen, on the guiding principle, that if 
a fact of the class A is true, a fact of the class B is true. 
The probability consists of the fraction whose numerator 
is the number of times in which both A and B are true, 
and whose denominator is the total number of times in 
which A is true, whether B is so or not. Instead of speak¬ 
ing of this as the probability of the inference, there is not 
the slightest objection to calling it the probability that, if 
A happens, B happens. But to speak of the probability 
of the event B, without naming the condition, really has no 
meaning at all. It is true that when it is perfectly obvious 
what condition is meant, the ellipsis may be permitted. But 
we should avoid contracting the habit of using language in 
this way (universal as the habit is), because it gives rise 


THE DOCTRINE OF CHANCES 


69 


to a vague way of thinking, as if the action of causation 
might either determine an event to happen or determine it 
not to happen, or leave it more or less free to happen or 
not, so as to give rise to an inherent chance in regard to its 
occurrence. 4 It is quite clear to me that some of the worst 
and most persistent errors in the use of the doctrine of 
chances have arisen from this vicious mode of expression. 5 


iv 

But there remains an important point to be cleared up. 
According to what has been said, the idea of probability 
essentially belongs to a kind of inference which is repeated 
indefinitely. An individual inference must be either true 
or false, and can show no effect of probability; and, there¬ 
fore, in reference to a single case considered in itself, prob¬ 
ability can have no meaning. Yet if a man had to choose 
between drawing a card from a pack containing twenty- 
five red cards and a black one, or from a pack containing 
twenty-five black cards and a red one, and if the drawing 
of a red card were destined to transport him to eternal 
felicity, and that of a black one to consign him to everlasting 
woe, it would be folly to deny that he ought to prefer the 
pack containing the larger portion of red cards, although, 
from the nature of the risk, it could not be repeated. It is 
not easy to reconcile this with our analysis of the conception 

4 Cf. pp. 179 ff. below. 

5 The conception of probability here set forth is substantially that first 
developed by Mr. Venn, in his Logic of Chance. Of course, a vague 
apprehension of the idea had always existed, but the problem was to make 
it perfectly clear, and to him belongs the credit of first doing this. 


7 o 


CHANCE AND LOGIC 


of chance. But suppose he should choose the red pack, 
and should draw the wrong card, what consolation would he 
have? He might say that he had acted in accordance with 
reason, but that would only show that his reason was abso¬ 
lutely worthless. And if he should choose the right card, 
how could he regard it as anything but a happy accident? 
He could not say that if he had drawn from the other pack, 
he might have drawn the wrong one, because an hypotheti¬ 
cal proposition such as, “ if A, then B,” means nothing with 
reference to a single case. Truth consists in the existence 
of a real fact corresponding to the true proposition. Corre¬ 
sponding to the proposition, “ if A, then B,” there may be 
the fact that whenever such an event as A happens such an 
event as B happens. But in the case supposed, which has 
no parallel as far as this man is concerned, there would be 
no real fact whose existence could give any truth to the 
statement that, if he had drawn from the other pack, he 
might have drawn a black card. Indeed, since the validity 
of an inference consists in the truth of the hypothetical 
proposition that if the premises be true the conclusion will 
also be true, and since the only real fact which can corre¬ 
spond to such a proposition is that whenever the antecedent 
is true the consequent is so also, it follows that there can 
be no sense in reasoning in an isolated case, at all. 

These considerations appear, at first sight, to dispose of 
the difficulty mentioned. Yet the case of the other side is 
not yet exhausted. Although probability will probably 
manifest its effect in, say, a thousand risks, by a certain 
proportion between the numbers of successes and failures, 
yet this, as we have seen, is only to say that it certainly will, 


THE DOCTRINE OF CHANCES 


7* 


at length, do so. Now the number of risks, the number of 
probable inferences, which a man draws in his whole life, 
is a finite one, and he cannot be absolutely certain that the 
mean result will accord with the probabilities at all. Tak¬ 
ing all his risks collectively, then, it cannot be certain that 
they will not fail, and his case does not differ, except in de¬ 
gree, from the one last supposed. It is an indubitable re¬ 
sult of the theory of probabilities that every gambler, if he 
continues long enough, must ultimately be ruined. Suppose 
he tries the martingale, which some believe infallible, and 
which is, as I am informed, disallowed in the gambling- 
houses. In this method of playing, he first bets say $1; 
if he loses it he bets $2; if he loses that he bets $4; if he 
loses that he bets $8; if he then gains he has lost 
1 + 2 + 4 = 7, and he has gained $1 more; and no matter 
how many bets he loses, the first one he gains will make 
him $1 richer than he was in the beginning. In that way, 
he will probably gain at first; but, at last, the time wall 
come when the run of luck is so against him that he will not 
have money enough to double, and must, therefore, let his 
bet go. This will probably happen before he has won as 
much as he had in the first place, so that this run against 
him will leave him poorer than he began; some time or other 
it will be sure to happen. It is true that there is always a 
possibility of his winning any sum the bank can pay, and 
we thus come upon a celebrated paradox that, though he is 
certain to be ruined, the value of his expectation calculated 
according to the usual rules (which omit this consideration) 
is large. But, whether a gambler plays in this way or any 
other, the same thing is true, namely, that if he plays long 


7 2 


CHANCE AND LOGIC 


enough he will be sure some time to have such a run against 
him as to exhaust his entire fortune. The same thing is 
true of an insurance company. Let the directors take the 
utmost pains to be independent of great conflagrations and 
pestilences, their actuaries can tell them that, according 
to the doctrine of chances, the time must come, at last, when 
their losses will bring them to a stop. They may tide over 
such a crisis by extraordinary means, but then they will 
start again in a weakened state, and the same thing will 
happen again all the sooner. An actuary might be inclined 
to deny this, because he knows that the expectation of his 
company is large, or perhaps (neglecting the interest upon 
money) is infinite. But calculations of expectations leave 
out of account the circumstance now under consideration, 
which reverses the whole thing. However, I must not be 
understood as saying that insurance is on this account un¬ 
sound, more than other kinds of business. All human af¬ 
fairs rest upon probabilities, and the same thing is true 
everywhere. If man were immortal he could be perfectly 
sure of seeing the day when everything in which he had 
trusted should betray his trust, and, in short, of coming 
eventually to hopeless misery. He would break down, at 
last, as every good fortune, as every dynasty, as every 
civilization does. In place of this we have death. 

But what, without death, would happen to every man, 
with death must happen to some man. At the same time, 
death makes the number of our risks, of our inferences, 
finite, and so makes their mean result uncertain. The very 
idea of probability and of reasoning rests on the assumption 
that this number is indefinitely great. We are thus landed 


THE DOCTRINE OF CHANCES 


73 


in the same difficulty as before, and I can see but one solu¬ 
tion of it. It seems to me that we are driven to this, that 
logicality inexorably requires that our interests shall not 
be limited. They must not stop at our own fate, but must 
embrace the whole community. This community, again, 
must not be limited, but must extend to all races of beings 
with whom we can come into immediate or mediate intel¬ 
lectual relation. It must reach, however vaguely, beyond 
this geological epoch, beyond all bounds. He who would 
not sacrifice his own soul to save the whole world, is, as it 
seems to me, illogical in all his inferences, collectively. 
Logic is rooted in the social principle. 

To be logical men should not be selfish; and, in point of 
fact, they are not so selfish as they are thought. The will¬ 
ful prosecution of one’s desires is a different thing from 
selfishness. The miser is not selfish; his money does him 
no good, and he cares for what shall become of it after his 
death. We are constantly speaking of our possessions on 
the Pacific, and of our destiny as a republic, where no per¬ 
sonal interests are involved, in a way which shows that we 
have wider ones. We discuss with anxiety the possible ex¬ 
haustion of coal in some hundreds of years, or the cooling- 
off of the sun in some millions, and show in the most popular 
of all religious tenets that we can conceive the possibility of 
a man’s descending into hell for the salvation of his fellows. 

Now, it is not necessary for logicality that a man should 
himself be capable of the heroism of self-sacrifice. It is 
sufficient that he should recognize the possibility of it, 
should perceive that only that man’s inferences who has it 
are really logical, and should consequently regard his own 


74 


CHANCE AND LOGIC 


as being only so far valid as they would be accepted by 
the hero. So far as he thus refers his inferences to that 
standard, he becomes identified with such a mind. 

This makes logicality'' attainable enough. Sometimes we 
can personally attain to heroism. The soldier who runs to 
scale a wall knows that he will probably be shot, but that 
is not all he cares for. He also knows that if all the regi¬ 
ment, with whom in feeling he identifies himself, rush for¬ 
ward at once, the fort will be taken. In other cases we 
can only imitate the virtue. The man whom we have sup¬ 
posed as having to draw from the two packs, who if he is 
not a logician will draw from the red pack from mere 
habit, will see, if he is logician enough, that he cannot be 
logical so long as he is concerned only with his own fate, 
but that that man who should care equally for what was 
to happen in all possible cases of the sort could act logi¬ 
cally, and would draw from the pack with the most red 
cards, and thus, though incapable himself of such sub¬ 
limity, our logician would imitate the effect of that man’s 
courage in order to share his logicality. 

But all this requires a conceived identification of one’s 
interests with those of an unlimited community. Now, 
there exist no reasons, and a later discussion will show that 
there can be no reasons, for thinking that the human race, 
or any intellectual race, will exist forever. On the other 
hand, there can be no reason against it; G and, fortunately, 
as the whole requirement is that we should have certain 

6 I do not here admit an absolutely unknowable. Evidence could show 
us what would probably be the case after any given lapse of time; and 
though a subsequent time might be assigned which that evidence might 
not cover, yet further evidence would cover it. 


THE DOCTRINE OF CHANCES 


75 


sentiments, there is nothing in the facts to forbid our having 
a hope, or calm and cheerful wish, that the community may 
last beyond any assignable date. 

It may seem strange that I should put forward three 
sentiments, namely, interest in an indefinite community, 
recognition of the possibility of this interest being made 
supreme, and hope in the unlimited continuance of intellec¬ 
tual activity, as indispensable requirements of logic. Yet, 
when we consider that logic depends on a mere struggle to 
escape doubt, which, as it terminates in action, must begin 
in emotion, and that, furthermore, the only cause of our 
planting ourselves on reason is that other methods of escap¬ 
ing doubt fail on account of the social impulse, why should 
we wonder to find social sentiment presupposed in 
reasoning? As for the other two sentiments which I find 
necessary, they are so only as supports and accessories of 
that. It interests me to notice that these three sentiments 
seem to be pretty much the same as that famous trio of 
Charity, Faith, and Hope, which, in the estimation of St. 
Paul, are the finest and greatest of spiritual gifts. Neither 
Old nor New Testament is a textbook of the logic of science, 
but the latter is certainly the highest existing authority in 
regard to the dispositions of heart which a man ought 
to have. 


v 

Such average statistical numbers as the number of in¬ 
habitants per square mile, the average number of deaths 
per week, tfie number of convictions per indictment, or, 
generally speaking, the numbers of x’s per y, where the x f s 


76 


CHANCE AND LOGIC 


are a class of things some or all of which are connected with 
another class of things, their y’s, I term relative numbers . 
Of the two classes of things to which a relative number 
refers, that one of which it is a number may be called its 
relate y and that one per which the numeration is made may 
be called its correlate. 

Probability is a kind of relative number; namely, it is 
the ratio of the number of arguments of a certain genus 
which carry truth with them to the total number of argu¬ 
ments of that genus, and the rules for the calculation of 
probabilities are very easily derived from this considera¬ 
tion. They may all be given here, since they are extremely 
simple, and it is sometimes convenient to know something 
of the elementary rules of calculation of chances. 

Rule I. Direct Calculation. — To calculate, directly, 
any relative number, say for instance the number of pas¬ 
sengers in the average trip of a street-car, we must proceed 
as follows: 

Count the number of passengers for each trip; add all 
these numbers, and divide by the number of trips. There 
are cases in which this rule may be simplified. Suppose 
we wish to know the number of inhabitants to a dwelling 
in New York. The same person cannot inhabit two dwell¬ 
ings. If he divide his time between two dwellings he ought 
to be counted a half-inhabitant of each. In this case we 
have only to divide the total number of the inhabitants of 
New York by the number of their dwellings, without the 
necessity of counting separately those which inhabit each 
one. A similar proceeding will apply wherever each in¬ 
dividual relate belongs to one individual correlate exclu- 


THE DOCTRINE OF CHANCES 


77 


sively. If we want the number of x’s per y, and no x be¬ 
longs to more than one y, we have only to divide the whole 
number of x’s of y’s by the number of y’s. Such a method 
would, of course, fail if applied to finding the average num¬ 
ber of street-car passengers per trip. We could not divide 
the total number of travelers by the number of trips, since 
many of them would have made many passages. 

To find the probability that from a given class of prem¬ 
ises, A, a given class of conclusions, B, follow, it is simply 
necessary to ascertain what proportion of the times in which 
premises of that class are true, the appropriate conclusions 
are also true. In other words, it is the number of cases 
of the occurrence of both the events A and B, divided by 
the total number of cases of the occurrence of the event A. 

Rule II. Addition of Relative Numbers . — Given two 
relative numbers having the same correlate, say the num¬ 
ber of x’s per y, and the number of s’s per y; it is required 
to find the number of x’s and s’s together per y. If there 
is nothing which is at once an x and a z to the same y , the 
sum of the two given numbers would give the required 
number. Suppose, for example, that we had given the aver¬ 
age number of friends that men have, and the average 
number of enemies, the sum of these two is the average 
number of persons interested in a man. On the other hand, 
it plainly would not do to add the average number of 
persons having constitutional diseases and over military 
age, to the average number exempted by each special cause 
from military service, in order to get the average number 
exempt in any way, since many are exempt in two or more 
ways at once. 


7§ 


CHANCE AND LOGIC 


This rule applies directly to probabilities, given the 
probability that two different and mutually exclusive events 
will happen under the same supposed set of circumstances. 
Given, for instance, the probability that if A then B, and 
also the probability that if A then C, then the sum of these 
two probabilities is the probability that if A then either B 
or C, so long as there is no event which belongs at once to 
the two classes B and C. 

Rule III. Multiplication of Relative Numbers. — Sup¬ 
pose that we have given the relative number of x’s per y; 
also the relative number of s’s per jc of y; or, to take a 
concrete example, suppose that we have given, first, the 
average number of children in families living in New York; 
and, second, the average number of teeth in the head of a 
New York child — then the product of these two numbers 
would give the average number of children’s teeth in a 
New York family. But this mode of reckoning will only 
apply in general under two restrictions. In the first place, 
it would not be true if the same child could belong to dif¬ 
ferent families, for in that case those children who belonged 
to several different families might have an exceptionally 
large or small number of teeth, which would affect the 
average number of children’s teeth in a family more than 
it would affect the average number of teeth in a child’s head. 
In the second place, the rule would not be true if different 
children could share the same teeth, the average number 
of children’s teeth being in that case evidently something 
different from the average number of teeth belonging to 
a child. 


THE DOCTRINE OF CHANCES 


79 


In order to apply this rule to probabilities, we must pro¬ 
ceed as follows: Suppose that we have given the proba¬ 
bility that the conclusion B follows from the premise A, B 
and A representing as usual certain classes of propositions. 
Suppose that we also knew the probability of an inference 
in which B should be the premise, and a proposition of a 
third kind, C, the conclusion. Here, then, we have the 
materials for the application of this rule. We have, first, 
the relative number of B’s per A. We next should have 
the relative number of C’s per B following from A. But 
the classes of propositions being so selected that the prob¬ 
ability of C following from any B in general is just the same 
as the probability of C’s following from one of those B’s 
which is deducible from an A, the two probabilities may 
be multiplied together, in order to give the probability of 
C following from A. The same restrictions exist as before. 
It might happen that the probability that B follows from A 
was affected by certain propositions of the class B follow¬ 
ing from several different propositions of the class A. But, 
practically speaking, all these restrictions are of very little 
consequence, and it is usually recognized as a principle 
universally true that the probability that, if A is true, B is, 
multiplied by the probability that, if B is true, C is, gives 
the probability that, if A is true, C is. 

There is a rule supplementary to this, of which great use 
is made. It is not universally valid, and the greatest cau¬ 
tion has to be exercised in making use of it — a double care, 
first, never to use it when it will involve serious error; and, 
second, never to fail to take advantage of it in cases in 
which it can be employed. This rule depends upon the fact 


8o 


CHANCE AND LOGIC 


that in very many cases the probability that C is true if 
B is, is substantially the same as the probability that C is 
true if A is. Suppose, for example, we have the average 
number of males among the children born in New York; 
suppose that we also have the average number of children 
born in the winter months among those born in New York. 
Now, we may assume without doubt, at least as a closely 
approximate proposition (and no very nice calculation 
would be in place in regard to probabilities), that the pro¬ 
portion of males among all the children born in New York 
is the same as the proportion of males born in summer in 
New York; and, therefore, if the names of all the children 
born during a year were put into an urn, we might multiply 
the probability that any name drawn would be the name 
of a male child by the probability that it would be the name 
of a child born in summer, in order to obtain the prob¬ 
ability that it would be the name of a male child born in 
summer. The questions of probability, in the treatises 
upon the subject, have usually been such as relate to balls 
drawn from urns, and games of cards, and so on, in which 
the question of the independence of events, as it is called — 
that is to say, the question of whether the probability of C, 
under the hypothesis B, is the same as its probability under 
the hypothesis A, has been very simple; but, in the appli¬ 
cation of probabilities to the ordinary questions of life, it 
is often an exceedingly nice question whether two events 
may be considered as independent with sufficient accuracy 
or not. In all calculations about cards it is assumed that 
the cards are thoroughly shuffled, which makes one deal 
quite independent of another. In point of fact the cards 


THE DOCTRINE OF CHANCES 81 

seldom are, in practice, shuffled sufficiently to make this 
true; thus, in a game of whist, in which the cards have 
fallen in suits of four of the same suit, and are so gathered 
up, they will lie more or less in sets of four of the same suit, 
and this will be true even after they are shuffled. At least 
some traces of this arrangement will remain, in consequence 
of which the number of “ short suits,” as they are called 
— that is to say, the number of hands in which the cards 
are very unequally divided in regard to suits — is smaller 
than the calculation would make it to be; so that, when 
there is a misdeal, where the cards, being thrown about the 
table, get very thoroughly shuffled, it is a common saying 
that in the hands next dealt out there are generally short 
suits. A few years ago a friend of mine, who plays whist 
a great deal, was so good as to count the number of spades 
dealt to him in 165 hands, in which the cards had been, if 
anything, shuffled better than usual. According to calcula¬ 
tion, there should have been 85 of these hands in which my 
friend held either three or four spades, but in point of fact 
there were 94, showing the influence of imperfect shuffling. 

According to the view here taken, these are the only 
fundamental rules for the calculation of chances. An addi¬ 
tional one, derived from a different conception of prob¬ 
ability, is given in some treatises, which if it be sound might 
be made the basis of a theory of reasoning. Being, as I 
believe it is, absolutely absurd, the consideration of it serves 
to bring us to the true theory; and it is for the sake of this 
discussion, which must be postponed to the next number, 
that I have brought the doctrine of chances to the reader’s 
attention at this early stage of our studies of the logic of 
science. 


FOURTH PAPER 


THE PROBABILITY OF INDUCTION 1 

i 

We have found mat every argument derives its force from 
the general truth of the class of inferences to which it be¬ 
longs; and that probability is the proportion of arguments 
carrying truth with them among those of any genus. This 
is most conveniently expressed in the nomenclature of the 
medieval logicians. They called the fact expressed by a 
premise an antecedent , and that which follows from it its 
consequent; while the leading principle, that every (or 
almost every) such antecedent is followed by such a con¬ 
sequent, they termed the consequeyicc. Using this lan¬ 
guage, we may say that probability belongs exclusively to 
consequences, and the probability of any consequence is 
the number of times in which antecedent and consequent 
both occur divided by the number of all the times in which 
the antecedent occurs. From this definition are deduced 
the following rules for the addition and multiplication of 
probabilities: 

Rule for the Addition of Probabilities. — Given the sepa¬ 
rate probabilities of two consequences having the same ante¬ 
cedent and incompatible consequents. Then the sum of 
these two numbers is the probability of the consequence, 

1 Popular Science Monthly, April, 1878. 

82 


THE PROBABILITY OF INDUCTION 83 

that from the same antecedent one or other of those con¬ 
sequents follows. 

Rule for the Multiplication of Probabilities . — Given the 
separate probabilities of the two consequences, “ If A then 
B,” and “ If both A and B, then C.” Then the product 
of the these two numbers is the probability of the conse¬ 
quence, “ If A, then both B and C.” 

Special Rule for the Multiplication of Independent Prob¬ 
abilities. — Given the separate probabilities of two conse¬ 
quences having the same antecedents, “ If A, then B,” and 
“If A, then C.” Suppose that these consequences are such 
that the probability of the second is equal to the probability 
of the consequence, “ If both A and B, then CP Then the 
product of the two given numbers is equal to the probability 
of the consequence, “ If A, then both B and C.” 

To show the working of these rules we may examine the 
probabilities in regard to throwing dice. What is the prob¬ 
ability of throwing a six with one die? The antecedent 
here is the event of throwing a die; the consequent, its 
turning up a six. As the die has six sides, all of which are 
turned up with equal frequency, the probability of turning 
up any one is £. Suppose two dice are thrown, what is 
the probability of throwing sixes? The probability of either 
coming up six is obviously the same when both are thrown 
as when one is thrown — namely, The probability that 
either will come up six when the other does is also the same 
as that of its coming up six whether the other does or not. 
The probabilities are, therefore, independent; and, by our 
rule, the probability that both events will happen together 
is the product of their several probabilities, or £ X What 


8 4 


CHANCE AND LOGIC 


is the probability of throwing deuce-ace? The probability 
that the first die will turn up ace and the second deuce is 
the same as the probability that both will turn up sixes — 
namely, the probability that the second will turn up 
ace and the first deuce is likewise gV, these two events — 
first, ace; second, deuce; and, second, ace; first, deuce — 
are incompatible. Hence the rule for addition holds, and 
the probability that either will come up ace and the other 
deuce is 3V T - §•* or pgr • 

In this way all problems about dice, etc., may be solved. 
When the number of dice thrown is supposed very large, 
mathematics (which may be defined as the art of making 
groups to facilitate numeration) comes to our aid with 
certain devices to reduce the difficulties. 

n 

The conception of probability as a matter of fact, i.e., as 
the proportion of times in which an occurrence of one kind 
is accompanied by an occurrence of another kind, is termed 
by Mr. Venn the materialistic view of the subject. But 
probability has often been regarded as being simply the 
degree of belief which ought to attach to a proposition, and 
this mode of explaining the idea is termed by Venn the 
conceptualistic view. Most writers have mixed the two 
conceptions together. They, first, define the probability of 
an event as the reason we have to believe that it has taken 
place, which is conceptualistic; but shortly after they state 
that it is the ratio of the number of cases favorable to the 
event to the total number of cases favorable or contrary, 


THE PROBABILITY OF INDUCTION 85 

and all equally possible. Except that this introduces the 
thoroughly unclear idea of cases equally possible in place 
of cases equally frequent, this is a tolerable statement of 
the materialistic view. The pure conceptualistic theory has 
been best expounded by Mr. De Morgan in his Formal 
Logic: or, the Calculus of Inference, Necessary and 
Probable. 

The great difference between the two analyses is, that 
the conceptualists refer probability to an event, while the 
materialists make it the ratio of frequency of events of a 
species to those of a genus over that species , thus giving it 
two terms instead of one . The opposition may be made to 
appear as follows: 

Suppose that we have two rules of inference, such that, 
of all the questions to the solution of which both can be 
applied, the first yields correct answers to ^0, and in¬ 
correct answers to the remaining while the second 
yields correct answers to xVo, and incorrect answers to the 
remaining -pfo. Suppose, further, that the two rules are 
entirely independent as to their truth, so that the second 
answers correctly of the questions which the first an¬ 
swers correctly, and also of the questions which the 
first answers incorrectly, and answers incorrectly the re¬ 
maining of the questions which the first answers 
correctly, and also the remaining j-fc of the questions which 
the first answers incorrectly. Then, of all the questions to 
the solution of which both rules can be applied — 








86 


CHANCE AND LOGIC 


both answer correctly 


93 

IOO 


.81 93 X 81 

of — or • ■ ■----; 

100 100 X 100 


the second answers correctly and the first incorrectly — of or 

IOO IOO 


7 81 

the second answers incorrectly and the first correctly — of — or 

100 100 


93 X 19 . 

100 x ioo’ 

7 X 81 
100 X ioo’ 


and both answer incorrectly 



100 


19 7 X 19 

— or —-—; 

100 100 x 100 


Suppose, now, that, in reference to any question, both 
give the same answer. Then (the questions being always 
such as are to be answered by yes or no), those in reference 
to which their answers agree are the same as those which 
both answer correctly together with those which both an¬ 


swer falsely, or - 93 - x . + - 7 - x - 19 - of all. The 

100 X 100 100 X 100 

proportion of those which both answer correctly out of those 
their answers to which agree is, therefore — 


' . 93 X 81 

100 X 100 03 X 81 

-QJ- -iii- 

93 X 81 7 X 19 (93 X 81) + (7 X 19). 

100 X 100 ~ 100 X 100 

This is, therefore, the probability that, if both modes of 
inference yield the same result, that result is correct. We 
may here conveniently make use of another mode of ex¬ 
pression. Probability is the ratio of the favorable cases to 
all the cases. Instead of expressing our result in terms of 
this ratio, we may make use of another — the ratio of 
favorable to unfavorable cases. This last ratio may be 
called the chance of an event. Then the chance of a true 
answer by the first mode of inference is and by the 
second is ^; and the chance of a correct answer from both, 
when they agree, is — 















THE PROBABILITY OF INDUCTION 87 

81 X 93 81 93 

-— or — x —, 

19 X 7 19 7 

or the product of the chances of each singly yielding a true 
answer. 

It will be seen that a chance is a quantity which may have 
any magnitude, however great. An event in whose favor 
there is an even chance, or j -, has a probability of An 
argument having an even chance can do nothing toward re¬ 
enforcing others, since according to the rule its combination 
with another would only multiply the chance of the latter 
by 1. 

Probability and chance undoubtedly belong primarily to 
consequences, and are relative to premises; but we may, 
nevertheless, speak of the chance of an event absolutely, 
meaning by that the chance of the combination of all argu¬ 
ments in reference to it which exist for us in the given state 
of our knowledge. Taken in this sense it is incontestable 
that the chance of an event has an intimate connection with 
the degree of our belief in it. Belief is certainly something 
more than a mere feeling; yet there is a feeling of believing, 
and this feeling does and ought to vary with the chance of 
the thing believed, as deduced from all the arguments. 
Any quantity which varies with the chance might, therefore, 
it would seem, serve as a thermometer for the proper in¬ 
tensity of belief. Among all such quantities there is one 
which is peculiarly appropriate. When there is a very great 
chance, the feeling of belief ought to be very intense. Ab¬ 
solute certainty, or an infinite chance, can never be attained 
by mortals, and this may be represented appropriately by 
an infinite belief. As the chance diminishes the feeling of 



88 


CHANCE AND LOGIC 


believing should diminish, until an even chance is reached, 
where it should completely vanish and not incline either 
toward or away from the proposition. When the chance 
becomes less, then a contrary belief should spring up and 
should increase in intensity as the chance diminishes, and 
as the chance almost vanishes (which it can never quite do) 
the contrary belief should tend toward an infinite intensity. 
Now, there is one quantity which, more simply than any 
other, fulfills these conditions; it is the logarithm of the 
chance. But there is another consideration which must, 
if admitted, fix us to this choice for our thermometer. It 
is that our belief ought to be proportional to the weight of 
evidence, in this sense, that two arguments which are en¬ 
tirely independent, neither weakening nor strengthening 
each other, ought, when they concur, to produce a belief 
equal to the sum of the intensities of belief which either 
would produce separately. Now, we have seen that the 
chances of independent concurrent arguments are to be 
multiplied together to get the chance of their combination, 
and, therefore, the quantities which best express the in¬ 
tensities of belief should be such that they are to be added 
when the chances are multiplied in order to produce the 
quantity which corresponds to the combined chance. Now, 
the logarithm is the only quantity which fulfills this condi¬ 
tion. There is a general law of sensibility, called Fechner’s 
psychophysical law. It is that the intensity of any sensa¬ 
tion is proportional to the logarithm of the external force 
which produces it. It is entirely in harmony with this law 
that the feeling of belief should be as the logarithm of the 
chance, this latter being the expression of the state of facts 
which produces the belief. 


THE PROBABILITY OF INDUCTION 89 

The rule for the combination of independent concurrent 
arguments takes a very simple form when expressed in 
terms of the intensity of belief, measured in the proposed 
way. It is this: Take the sum of all the feelings of belief 
which would be produced separately by all the arguments 
pro, subtract from that the similar sum for arguments con, 
and the remainder is the feeling of belief which we ought 
to have on the whole. This is a proceeding which men 
often resort to, under the name of balancing reasons . 

These considerations constitute an argument in favor of 
the conceptualistic view. The kernel of it is that the con¬ 
joint probability of all the arguments in our possession, 
with reference to any fact, must be intimately connected 
with the just degree of our belief in that fact; and this point 
is supplemented by various others showing the consistency 
of the theory with itself and with the rest of our knowledge. 

But probability, to have any value at all, must express a 
fact. It is, therefore, a thing to be inferred upon evidence. 
Let us, then, consider for a moment the formation of a be¬ 
lief of probability. Suppose we have a large bag of beans 
from which one has been secretly taken at random and 
hidden under a thimble. We are now to form a probable 
judgment of the color of that bean, by drawing others singly 
from the bag and looking at them, each one to be thrown 
back, and the whole well mixed up after each drawing. 
Suppose the first drawing is white and the next black. We 
conclude that there is not an immense preponderance of 
either color, and that there is something like an even chance 
that the bean under the thimble is black. But this judg¬ 
ment may be altered by the next few drawings. When we 


90 


CHANCE AND LOGIC 


have drawn ten times, if 4, 5, or 6, are white, we have more 
confidence that the chance is even. When we have drawn 
a thousand times, if about half have been white, we have 
great confidence in this result. We now feel pretty sure 
that, if we were to make a large number of bets upon the 
color of single beans drawn from the bag, we could approxi¬ 
mately insure ourselves in the long run by betting each time 
upon the white, a confidence which would be entirely want¬ 
ing if, instead of sampling the bag by 1,000 drawings, we 
had done so by only two. Now, as the whole utility of 
probability is to insure us in the long run, and as that assur¬ 
ance depends, not merely on the value of the chance, but 
also on the accuracy of the evaluation, it follows that we 
ought not to have the same feeling of belief in reference 
to all events of which the chance is even. In short, to ex¬ 
press the proper state of our belief, not one number but two 
are requisite, the first depending on the inferred proba¬ 
bility, the second on the amount of knowledge on which 
that probability is based. 2 It is true that when our knowl¬ 
edge is very precise, when we have made many drawings 
from the bag, or, as in most of the examples in the books, 
when the total contents of the bag are absolutely known, 
the number which expresses the uncertainty of the assumed 
probability and its liability to be changed by further ex¬ 
perience may become insignificant, or utterly vanish. But, 
when our knowledge is very slight, this number may be even 
more important than the probability itself; and when we 
have no knowledge at all this completely overwhelms the 

2 Strictly we should need an infinite series of numbers each depending 
on the probable error of the last. 


THE PROBABILITY OF INDUCTION 


9 * 


other, so that there is no sense in saying that the chance 
of the totally unknown event is even (for what expresses 
absolutely no fact has absolutely no meaning), and what 
ought to be said is that the chance is entirely indefinite. 
We thus perceive that the conceptualistic view, though 
answering well enough in some cases, is quite inadequate. 

Suppose that the first bean which we drew from our 
bag were black. That would constitute an argument, no 
matter how slender, that the bean under the thimble was 
also black. If the second bean were also to turn out black, 
that would be a second independent argument reenforcing 
the first. If the whole of the first twenty beans drawn 
should prove black, our confidence that the hidden bean 
was black would justly attain considerable strength. But 
suppose the twenty-first bean were to be white and that 
we were to go on drawing until we found that we had drawn 
1,010 black beans and 990 white ones. We should conclude 
that our first twenty beans being black was simply an 
extraordinary accident, and that in fact the proportion of 
white beans to black was sensibly equal, and that it was an 
even chance that the hidden bean was black. Yet accord¬ 
ing to the rule of balancing reasons , since all the drawings 
of black beans are so many independent arguments in favor 
of the one under the thimble being black, and all the white 
drawings so many against it, an excess of twenty black 
beans ought to produce the same degree of belief that the 
hidden bean was black, whatever the total number drawn. 

In the conceptualistic view of probability, complete igno¬ 
rance, where the judgment ought not to swerve either toward 
or away from the hypothesis, is represented by the prob¬ 
ability ^. 3 

3 “Perfect indecision, belief inclining neither way, an even chance. 5 ’ — 
De Morgan, p. 182. 


92 CHANCE AND LOGIC 

But let us suppose that we are totally ignorant what 
colored hair the inhabitants of Saturn have. Let us, then, 
take a color-chart in which all possible colors are shown 
shading into one another by imperceptible degrees. In 
such a chart the relative areas occupied by different classes 
of colors are perfectly arbitrary. Let us inclose such an 
area with a closed line, and ask what is the chance on con- 
ceptualistic principles that the color of the hair of the 
inhabitants of Saturn falls within that area? The answer 
cannot be indeterminate because we must be in some state 
of belief; and, indeed, conceptualistic writers do not admit 
indeterminate probabilities. As there is no certainty in 
the matter, the answer lies between zero and unity . As no 
numerical value is afforded by the data, the number must 
be determined by the nature of the scale of probability 
itself, and not by calculation from the data. The answer 
can, therefore, only be one-half, since the judgment should 
neither favor nor oppose the hypothesis. What is true of 
this area is true of any other one; and it will equally be 
true of a third area which embraces the other two. But 
the probability for each of the smaller areas being one-half, 
that for the larger should be at least unity, which is absurd. 

hi 

All our reasonings are of two kinds: i. Explicative, ana¬ 
lytic, or deductive; 2. Amplifiative, synthetic, or (loosely 
speaking) inductive . In explicative reasoning, certain facts 
are first laid down in the premises. These facts are, in 
every case, an inexhaustible multitude, but they may often 


THE PROBABILITY OF INDUCTION 


93 


be summed up in one simple proposition by means of some 
regularity which runs through them all. Thus, take the 
proposition that Socrates was a man; this implies (to go no 
further) that during every fraction of a second of his whole 
life (or, if you please, during the greater part of them) he 
was a man. He did not at one instant appear as a tree 
and at another as a dog; he did not flow into water, or ap¬ 
pear in two places at once; you could not put your finger 
through him as if he were an optical image, etc. Now, 
the facts being thus laid down, some order among some of 
them, not particularly made use of for the purpose of stat¬ 
ing them, may perhaps be discovered; and this will enable 
us to throw part or all of them into a new statement, the 
possibility of which might have escaped attention. Such 
a statement will be the conclusion of an analytic inference. 
Of this sort are all mathematical demonstrations. But syn¬ 
thetic reasoning is of another kind. In this case the facts 
summed up in the conclusion are not among those stated 
in the premises. They are different facts, as when one 
sees that the tide rises m times and concludes that it will 
rise the next time. These are the only inferences which 
increase our real knowledge, however useful the others 
may be. 

In any problem in probabilities, we have given the rela¬ 
tive frequency of certain events, and we perceive that in 
these facts the relative frequency of another event is given 
in a hidden way. This being stated makes the solution. 
This is, therefore, mere explicative reasoning, and is evi¬ 
dently entirely inadequate to the representation of synthetic 
reasoning, which goes out beyond the facts given in the 


94 


CHANCE AND LOGIC 


premises. There is, therefore, a manifest impossibility in 
so tracing out any probability for a synthetic conclusion. 

Most treatises on probability contain a very different 
doctrine. They state, for example, that if one of the 
ancient denizens of the shores of the Mediterranean, who 
had never heard of tides, had gone to the bay of Biscay, 
and had there seen the tide rise, say m times, he could know 
that there was a probability equal to 

m + i 
m + 2 

that it would rise the next time. In a well-known work 
by Quetelet, much stress is laid on this, and it is made the 
foundation of a theory of inductive reasoning. 

But this solution betrays its origin if we apply it to the 
case in which the man has never seen the tide rise at all; 
that is, if we put m = o. In this case, the probability that 
it will rise the next time comes out or, in other words, 
the solution involves the conceptualistic principle that there 
is an even chance of a totally unknown event. The manner 
in which it has been reached has been by considering a 
number of urns all containing the same number of balls, 
part white and part black. One urn contains all white 
balls, another one black and the rest white, a third two 
black and the rest white, and so on, one urn for each pro¬ 
portion, until an urn is reached containing only black balls. 
But the only possible reason for drawing any analogy be¬ 
tween such an arrangement and that of Nature is the prin¬ 
ciple that alternatives of which we know nothing must be 
considered as equally probable. But this principle is ab¬ 
surd. There is an indefinite variety of ways of enumerat- 



THE PROBABILITY OF INDUCTION 


95 


ing the different possibilities, which, on the application of 
this principle, would give different results. If there be any 
way of enumerating the possibilities so as to make them 
all equal, it is not that from which this solution is derived, 
but is the following: Suppose we had an immense granary 
filled with black and white balls well mixed up; and sup¬ 
pose each urn were filled by taking a fixed number of balls 
from this granary quite at random. The relative number 
of white balls in the granary might be anything, say one in 
three. Then in one-third of the urns the first ball would 
be white, and in two-thirds black. In one-third of those 
urns of which the first ball was white, and also in one-third 
of those in which the first ball was black, the second ball 
would be white. In this way, we should have a distribu¬ 
tion like that shown in the following table, where w stands 
for a white ball and b for a black one. The reader can, 
if he chooses, verify the table for himself. 


wwww. 






wwwb. 

wwbw. 

wbww. 

bwww. 



wwwb. 

wwbw. 

wbww. 

bwww. 



wwbb. 

wbwb. 

bwwb. 

wbbw. 

bwbw. 

bbww. 

wwbb. 

wbwb. 

bwwb. 

wbbw. 

bwbw. 

bbww. 

wwbb. 

wbwb. 

bwwb. 

wbbw. 

bwbw. 

bbww. 

wwbb. 

wbwb. 

bwwb. 

wbbw. 

bwbw. 

bbww. 

wbbb. 

bwbb. 

bbwb. 

bbbw. 



wbbb. 

bwbb. 

bbwb. 

bbbw. 


• 

wbbb. 

bwbb. 

bbwb. 

bbbw. 



wbbb. 

bwbb. 

bbwb. 

bbbw. 




CHANCE AND LOGIC 


96 


wbbb. 

bwbb. 

bbwb. 

bbbw. 

wbbb. 

bwbb. 

bbwb. 

bbbw. 

wbbb. 

bwbb. 

bbwb. 

bbbw. 

wbbb. 

bwbb. 

bbwb. 

bbbw. 


bbbb. In the second group, where there is one b, there 
bbbb. are two sets just alike; in the third there are 4, in 
bbbb. the fourth 8, and in the fifth 16, doubling every 
bbbb. time. This is because we have supposed twice as 
bbbb. many black balls in the granary as white ones; had 
bbbb. we supposed 10 times as many, instead of 
bbbb. 

bbbb. , 1, 2, 4, 8, 16 

bbbb. 

bbbb. sets we should have had 
bbbb. 

bbbb. 1, 10, 100, 1000, 10000 

bbbb. 

bbbb. sets; on the other hand, had the numbers of black 
bbbb. and white balls in the granary been even, there 
bbbb. would have been but one set in each group. Now 
suppose two balls were drawn from one of these urns and 
were found to be both white, what would be the probability 
of the next one being white? If the two drawn out were 
the first two put into the urns, and the next to be drawn 
out were the third put in, then the probability of this third 
being white would be the same whatever the colors of the 
first two, for it has been supposed that just the same pro¬ 
portion of urns has the third ball white among those which 
have the first two white-white , white-black , black-white , 


THE PROBABILITY OF INDUCTION 


97 


and black-black. Thus, in this case, the chance of the third 
ball being white would be the same whatever the first two 
were. But, by inspecting the table, the reader can see that 
in each group all orders of the balls occur with equal fre¬ 
quency, so that it makes no difference whether they are 
drawn out in the order they were put in or not. Hence the 
colors of the balls already drawn have no influence on the 
probability of any other being white or black. 

Now, if there be any way of enumerating the possibilities 
of Nature so as to make them equally probable, it is clearly 
one which should make one arrangement or combination 
of the elements of Nature as probable as another, that is, 
a distribution like that we have supposed, and it, therefore, 
appears that the assumption that any such thing can be 
done, leads simply to the conclusion that reasoning from 
past to future experience is absolutely worthless. In fact, 
the moment that you assume that the chances in favor of 
that of which we are totally ignorant are even, the problem 
about the tides does not differ, in any arithmetical particu¬ 
lar, from the case in which a penny (known to be equally 
likely to come up heads and tails) should turn up heads 
m times successively. In short, it would be to assume that 
Nature is a pure chaos, or chance combination of inde¬ 
pendent elements, in which reasoning from one fact to an¬ 
other would be impossible; and since, as we shall hereafter 
see, there is no judgment of pure observation without reason¬ 
ing, it would be to suppose all human cognition illusory 
and no real knowledge possible. It would be to suppose 
that if we have found the order of Nature more or less 
regular in the past, this has been by a pure run of luck which 


98 


CHANCE AND LOGIC 


we may expect is now at an end. Now, it may be we have 
no scintilla of proof to the contrary, but reason is unneces¬ 
sary in reference to that belief which is of all the most 
settled, which nobody doubts or can doubt, and which he 
who should deny would stultify himself in so doing. 

The relative probability of this or that arrangement of 
Nature is something which we should have a right to talk 
about if universes were as plenty as blackberries, if we 
could put a quantity of them in a bag, shake them well up, 
draw out a sample, and examine them to see what propor¬ 
tion of them had one arrangement and what proportion 
another. But, even in that case, a higher universe would 
contain us, in regard to whose arrangements the conception 
of probability could have no applicability. 


iv 

We have examined the problem proposed by the con- 
ceptualists, which, translated into clear language, is this: 
Given a synthetic conclusion; required to know out of all 
possible states of things how many will accord, to any as¬ 
signed extent, with this conclusion; and we have found 
that it is only an absurd attempt to reduce synthetic to 
analytic reason, and that no definite solution is possible. 

But there is another problem in connection with this sub¬ 
ject. It is this: Given a certain state of things, required 
to know what proportion of all synthetic inferences relating 
to it will be true within a given degree of approximation. 
Now, there is no difficulty about this problem (except for 
its mathematical complication); it has been much studied, 


THE PROBABILITY OF INDUCTION 


99 


and the answer is perfectly well known. And is not this, 
after all, what we want to know much rather than the other? 
Why should we want to know the probability that the fact 
will accord with our conclusion? That implies that we 
are interested in all possible worlds, and not merely the one 
in which we find ourselves placed. Why is it not much 
more to the purpose to know the probability that our con¬ 
clusion will accord with the fact? One of these questions 
is the first above stated and the other the second, and I 
ask the reader whether, if people, instead of using the word 
probability without any clear apprehension of their own 
meaning, had always spoken of relative frequency, they 
could have failed to see that what they wanted was not to 
follow along the synthetic procedure with an analytic one, 
in order to find the probability of the conclusion; but, on 
the contrary, to begin with the fact at which the synthetic 
inference aims, and follow back to the facts it uses for 
premises in order to see the probability of their being such 
as will yield the truth. 

As we cannot have an urn with an infinite number of 
balls to represent the inexhaustibleness of Nature, let us 
suppose one with a finite number, each ball being thrown 
back into the urn after being drawn out, so that there is 
no exhaustion of them. Suppose one ball out of three is 
white and the rest black, and that four balls are drawn. 
Then the table on pages 95-96 represents the relative fre¬ 
quency of the different ways in which these balls might 
be drawn. It will be seen that if we should judge by these 
four balls of the proportion in the urn, 32 times out of 81 
we should find it and 24 times out of 81 we should find it 


100 


CHANCE AND LOGIC 


the truth being To extend this table to high numbers 
would be great labor, but the mathematicians have found 
some ingenious ways of reckoning what the numbers would 
be. It is found that, if the true proportion of white balls 
is p, and 5 balls are drawn, then the error of the proportion 
obtained by the induction will be — 

half the time within 

9 times out of io within 

99 times out of ioo within 

999 times out of i,ooo within 

9,999 times out of 10,000 within 

9,999,999,999 times out of 10,000,000,000 within 4.77 y/ ^ —— 

/ 

The use of this may be illustrated by an example. By 
the census of 1870, it appears that the proportion of males 
among native white children under one year old was 0.5082, 
while among colored children of the same age the proportion 
was only 0.4977. The difference between these is 0.0105, 
or about one in a 100. Can this be attributed to chance, 
or would the difference always exist among a great number 
of white and colored children under like circumstances? 
Here p may be taken at hence 2 p (1— p) is also The 
number of white children counted was near 1,000,000; 
hence the fraction whose square-root is to be taken is about 
?(j" ao oQo* The root is about and this multiplied by 

0.477 gives about 0.0003 as the probable error in the ratio 


0.477 


^ / 2 p(l - p) 

.63 

, S!I 'JlMl.zIl 
, 3l8v /M!Lzf) 

/ 2 p(l - p) 


2-751 


!o/h( T — 










THE PROBABILITY OF INDUCTION 


IOI 


of males among the whites as obtained from the induction. 
The number of black children was about 150,000, which 
gives 0.0008 for the probable error. We see that the actual 
discrepancy is ten times the sum of these, and such a result 
would happen, according to our table, only once out of 
10,000,000,000 censuses, in the long run. 

It may be remarked that when the real value of the prob¬ 
ability sought inductively is either very large or very small, 
the reasoning is more secure. Thus, suppose there were 
in reality one white ball in 100 in a certain urn, and we 
were to judge of the number by 100 drawings. The prob¬ 
ability of drawing no white ball would be that of 

drawing one white ball would be ; that of drawing two 
would be that of drawing three would be 

that of drawing four would be xjfo; that of drawing five 
would be only xoVo? etc. Thus we should be tolerably cer¬ 
tain of not being in error by more than one ball in 100. 

It appears, then, that in one sense we can, and in another 
we cannot, determine the probability of synthetic inference. 
When I reason in this way: 

Ninety-nine Cretans in a hundred are liars; 

But Epimenides is a Cretan; 

Therefore, Epimenides is a liar: — 

I know that reasoning similar to that would carry truth 99 
times in 100. But when I reason in the opposite direction: 

Minos, Sarpedon, Rhadamanthus, Deucalion, and Epi¬ 
menides, are all the Cretans I can think of; 

But these were all atrocious liars, 

Therefore, pretty much all Cretans must have been liars; 
I do not in the least know how often such reasoning would 








102 


CHANCE AND LOGIC 


carry me right. On the other hand, what I do know is 
that some definite proportion of Cretans must have been 
liars, and that this proportion can be probably approximated 
to by an induction from five or six instances. Even in the 
worst case for the probability of such an inference, that 
in which about half the Cretans are liars, the ratio so ob¬ 
tained would probably not be in error by more than So 
much I know; but, then, in the present case the inference 
is that pretty much all Cretans are liars, and whether there 
may not be a special improbability in that I do not know. 

v 

Late in the last century, Immanuel Kant asked the ques¬ 
tion, “ How are synthetical judgments a priori possible? ” 
By synthetical judgments he meant such as assert positive 
fact and are not mere affairs of arrangement; in short, 
judgments of the kind which synthetical reasoning produces, 
and which analytic reasoning cannot yield. By a priori 
judgments he meant such as that all outward objects are in 
space, every event has a cause, etc., propositions which 
according to him can never be inferred from experience. 
Not so much by his answer to this question as by the mere 
asking of it, the current philosophy of that time was shat¬ 
tered and destroyed, and a new epoch in its history was 
begun. But before asking that question he ought to have 
asked the more general one, “ How are any synthetical 
judgments at all possible? ” How is it that a man can ob¬ 
serve one fact and straightway pronounce judgment con¬ 
cerning another different fact not involved in the first? 


THE PROBABILITY OF INDUCTION 


103 


Such reasoning, as we have seen, has, at least in the usual 
sense of the phrase, no definite probability; how, then, 
can it add to our knowledge? This is a strange paradox; 
the Abbe Gratry says it is a miracle, and that every true 
induction is an immediate inspiration from on high. 4 I 
respect this explanation far more than many a pedantic 
attempt to solve the question by some juggle with proba¬ 
bilities, with the forms of syllogism, or what not. I re¬ 
spect it because it shows an appreciation of the depth of 
the problem, because it assigns an adequate cause, and be¬ 
cause it is intimately connected — as the true account 
should be — with a general philosophy of the universe. 
At the same time, I do not accept this explanation, because 
an explanation should tell how a thing is done, and to as¬ 
sert a perpetual miracle seems to be an abandonment of all 
hope of doing that, without sufficient justification. 

It will be interesting to see how the answer which Kant 
gave to his question about synthetical judgments a priori 
will appear if extended to the question of synthetical judg¬ 
ments in general. That answer is, that synthetical judg¬ 
ments a priori are possible because whatever is universally 
true is involved in the conditions of experience. Let us 
apply this to a general synthetical reasoning. I take from 
a bag a handful of beans; they are all purple, and I infer 
that all the beans in the bag are purple. How can I do 
that? Why, upon the principle that whatever is univer¬ 
sally true of my experience (which is here the appearance 

4 Logique. The same is true, according to him, of every performance 
of a differentiation, but not of integration. He does not tell us whether 
it is the supernatural assistance which makes the former process so 
much the easier. 


104 


CHANCE AND LOGIC 


of these different beans) is involved in the condition of 
experience. The condition of this special experience is 
that all these beans were taken from that bag. According 
to Kant’s principle, then, whatever is found true of all the 
beans drawn from the bag must find its explanation in 
some peculiarity of the contents of the bag. This is a 
satisfactory statement of the principle of induction. 

When we draw a deductive or analytic conclusion, our 
rule of inference is that facts of a certain general character 
are either invariably or in a certain proportion of cases 
accompanied by facts of another general character. Then 
our premise being a fact of the former class, we infer with 
certainty or with the appropriate degree of probability 
the existence of a fact of the second class. But the rule 
for synthetic inference is of a different kind. When we 
sample a bag of beans we do not in the least assume that 
the fact of some beans being purple involves the necessity 
or even the probability of other beans being so. On the 
contrary, the conceptualistic method of treating probabili¬ 
ties, which really amounts simply to the deductive treat¬ 
ment of them, when rightly carried out leads to the result 
that a synthetic inference has just an even chance in its 
favor, or in other words is absolutely worthless. The color 
of one bean is entirely independent of that of another. But 
synthetic inference is founded upon a classification of facts, 
not according to their characters, but according to the man¬ 
ner of obtaining them. Its rule is, that a number of facts 
obtained in a given way will in general more or less re¬ 
semble other facts obtained in the same way; or, experi¬ 
ences whose conditions are the same will have the same 
general characters. 


THE PROBABILITY OF INDUCTION 


105 


In the former case, we know that premises precisely 
similar in form to those of the given ones will yield true 
conclusions, just once in a calculable number of times. In 
the latter case, we only know that premises obtained under 
circumstances similar to the given ones (though perhaps 
themselves very different) will yield true conclusions, at 
least once in a calculable number of times. We may ex¬ 
press this by saying that in the case of analytic inference 
we know the probability of our conclusion (if the premises 
are true), but in the case of synthetic inferences we only 
know the degree of trustworthiness of our proceeding. As 
all knowledge comes from synthetic inference, we must 
equally infer that all human certainty consists merely in 
our knowing that the processes by which our knowledge 
has been derived are such as must generally have led to 
true conclusions. 

Though a synthetic inference cannot by any means be 
reduced to deduction, yet that the rule of induction will 
hold good in the long run may be deduced from the principle 
that reality is only the object of the final opinion to which 
sufficient investigation would lead. That belief gradually 
tends to fix itself under the influence of inquiry is, indeed, 
one of the facts with which logic sets out. 


FIFTH PAPER 


THE ORDER OF NATURE 1 


i 

Any proposition whatever concerning the order of Nature 
must touch more or less upon religion. In our day, belief, 
even in these matters, depends more and more upon the 
observation of facts. If a remarkable and universal order¬ 
liness be found in the universe, there must be some cause 
for this regularity, and science has to consider what hy¬ 
potheses might account for the phenomenon. One way of 
accounting for it, certainly, would be to suppose that the 
world is ordered by a superior power. But if there is 
nothing in the universal subjection of phenomena to laws, 
nor in the character of those laws themselves (as being 
benevolent, beautiful, economical, etc.), which goes to prove 
the existence of a governor of the universe, it is hardly to 
be anticipated that any other sort of evidence will be found 
to weigh very much with minds emancipated from the tyr¬ 
anny of tradition. 

Nevertheless, it cannot truly be said that even an abso¬ 
lutely negative decision of that question could altogether 
destroy religion, inasmuch as there are faiths in which, 
however much they differ from our own, we recognize those 
essential characters which make them worthy to be called 
religions, and which, nevertheless, do not postulate an 

1 Popular Science Monthly, June, 1878. 

106 


THE ORDER OF NATURE 


107 


actually existing Deity. That one, for instance, which has 
had the most numerous and by no means the least intelligent 
following of any on earth, teaches that the Divinity in his 
fiighest perfection is wrapped away from the world in a 
state of profound and eternal sleep, which really does not 
differ from non-existence, whether it be called by that name 
or not. No candid mind who has followed the writings of 
M. Vacherot can well deny that his religion is as earnest 
as can be. He worships the Perfect, the Supreme Ideal; 
but he conceives that the very notion of the Ideal is re¬ 
pugnant to its real existence. 2 In fact, M. Vacherot finds 
it agreeable to his reason to assert that non-existence 
is an essential character of the perfect, just as St. 
Anselm and Descartes found it agreeable to theirs to assert 
the extreme opposite. I confess that there is one respect in 
which either of these positions seems to me more congruous 
with the religious attitude than that of a theology which 
stands upon evidences; for as soon as the Deity presents 
himself to either Anselm or Vacherot, and manifests his 
glorious attributes, whether it be in a vision of the night 
or day, either of them recognizes his adorable God, and 
sinks upon his knees at once; whereas the theologian of 
evidences will first demand that the divine apparition shall 
identify himself, and only after having scrutinized his cre¬ 
dentials and weighed the probabilities of his being found 
among the totality of existences, will he finally render his 
circumspect homage, thinking that no characters can be 
adorable but those which belong to a real thing. 

If we could find out any general characteristic of the 

* [See Santayana, Reason in Religion .] 


108 CHANCE AND LOGIC 

universe, any mannerism in the ways of Nature, any law 
everywhere applicable and universally valid, such a dis¬ 
covery would be of such singular assistance to us in all our 
future reasoning, that it would deserve a place almost at 
the head of the principles of logic. On the other hand, 
if it can be shown that there is nothing of the sort to find 
out, but that every discoverable regularity is of limited 
range, this again will be of logical importance. What sort 
of a conception we ought to have of the universe, how to 
think of the ensemble of things, is a fundamental problem 
in the theory of reasoning. 

n 

It is the legitimate endeavor of scientific men now, as it 
was twenty-three hundred years ago, to account for the 
formation of the solar system and of the cluster of stars 
which forms the galaxy, by the fortuitous concourse of 
atoms. The greatest expounder of this theory, when asked 
how he could write an immense book on the system of the 
world without one mention of its author, replied, very 
logically, “Je n’avais pas besoin de cette hypothese-la.” 
But, in truth, there is nothing atheistical in the theory, 
any more than there was in this answer. Matter is sup¬ 
posed to be composed of molecules which obey the laws of 
mechanics and exert certain attractions upon one another; 
and it is to these regularities (which there is no attempt to 
account for) that general arrangement of the solar system 
would be due, and not to hazard. 

If any one has ever maintained that the universe is a 
pure throw of the dice, the theologians have abundantly 


THE ORDER OF NATURE 


109 


refuted him. “ How often,” says Archbishop Tillotson, 
“ might a man, after he had jumbled a set of letters in a 
bag, fling them out upon the ground before they would 
fall into an exact poem, yea, or so much as make a good 
discourse in prose! And may not a little book be as easily 
made by chance as this great volume of the world? ” The 
chance world here shown to be so different from that in 
which we live would be one in which there were no laws, 
the characters of different things being entirely indepen¬ 
dent; so that, should a sample of any kind of objects ever 
show a prevalent character, it could only be by accident, 
and no general proposition could ever be established. 
Whatever further conclusions we may come to in regard 
to the order of the universe, thus much may be regarded 
as solidly established, that the world is not a mere chance- 
medley. 

But whether the world makes an exact poem or not, is 
another question. When we look up at the heavens at 
night, we readily perceive that the stars are not simply 
splashed on to the celestial vault; but there does not seem 
to be any precise system in their arrangement either. It 
will be worth our while, then, to inquire into the degree of 
orderliness in the universe; and, to begin, let us ask whether 
the world we live in is any more orderly than a purely 
chance-world would be. 

Any uniformity, or law of Nature, may be stated in the 
form, “Every A is B ”; as, every ray of light is a non- 
curved line, every body is accelerated toward the earth’s 
center, etc. This is the same as to say, “ There does not 
exist any A which is not B ”; there is no curved ray; there 


IIO 


CHANCE AND LOGIC 


is no body not accelerated toward the earth; so that the 
uniformity consists in the non-occurrence in Nature of a 
certain combination of characters (in this case, the com¬ 
bination of being A with being non-B ). 3 And, conversely, 
every case of the non-occurrence of a combination of char¬ 
acters would constitute a uniformity in Nature. Thus, sup¬ 
pose the quality A is never found in combination with the 
quality C: for example, suppose the quality of idiocy is 
never found in combination with that of having a well- 
developed brain. Then nothing of the sort A is of the sort 
C, or everything of the sort A is of the sort non-C (or say, 
every idiot has an ill-developed brain), which, being some¬ 
thing universally true of the A’s, is a uniformity in the 
world. Thus we see that, in a world where there were no 
uniformities, no logically possible combination of characters 
would be excluded, but every combination would exist in 
some object. But two objects not identical must differ in 
some of their characters, though it be only in the character 
of being in such-and-such a place. Hence, precisely the 
same combination of characters could not be found in two 
different objects; and, consequently, in a chance-world every 
combination involving either the positive or negative of 
every character would belong to just one thing. Thus, if 
there were but five simple characters in such a world , 4 we 
might denote them by A, B, C, D, E, and their negatives 

3 For the present purpose, the negative of a character is to be con¬ 
sidered as much a character as the positive, for a uniformity may either 
be affirmative or negative. I do not say that no distinction can be drawn 
between positive and negative uniformities. 

4 There being 5 simple characters, with their negatives, they could 
be compounded in various ways so as to make 241 characters in all, with¬ 
out counting the characters existence and non-existence, which make up 


THE ORDER OF NATURE ill 

by a, b, c, d, e; and then, as there would be 2 5 or 32 different 
combinations of these characters, completely determinate 
in reference to each of them, that world would have just 32 
objects in it, their characters being as in the following 
table: 

Table I. 


ABCDE 

AbCDE 

aBCDE 

abCDE 

ABCDe 

AbCDe 

aBCDe 

abCDe 

ABCdE 

AbCdE 

aBCdE 

abCdE 

ABCde 

AbCde 

aBCde 

abCde 

ABcDE 

AbcDE 

aBcDE 

abcDE 

ABcDe 

AbcDe 

aBcDe 

abcDe 

ABcdE 

AbcdE 

aBcdE 

abcdE 

ABcde 

Abcde 

aBcde 

abcde 


For example, if the five primary characters were hard , 
sweet, fragrant, green, bright, there would be one object 
which reunited all these qualities, one which was hard, 
sweet, fragrant, and green, but not bright; one which was 
hard, sweet, fragrant, and bright, but not green; one which 
was hard, sweet, and fragrant, but neither green nor bright; 
and so on through all the combinations. 

This is what a thoroughly chance-world would be like, 
and certainly nothing could be imagined more systematic. 
When a quantity of letters are poured out of a bag, the 
appearance of disorder is due to the circumstance that the 
phenomena are only partly fortuitous. The laws of space 
are supposed, in that case, to be rigidly preserved, and 
there is also a certain amount of regularity in the forma¬ 
tion of the letters. The result is that some elements are 


I I 2 


CHANCE AND LOGIC 


orderly and some are disorderly, which is precisely what 
we observe in the actual world. Tillotson, in the passage 
of which a part has been quoted, goes on to ask, “ How long 
might 20,000 blind men which should be sent out from 
the several remote parts of England, wander up and down 
before they would all meet upon Salisbury Plains, and fall 
into rank and file in the exact order of an army? And yet 
this is much more easy to be imagined than how the in¬ 
numerable blind parts of matter should rendezvous them¬ 
selves into a world.” This is very true, but in the actual 
world the blind men are, as far as we can see, not drawn up 
in any particular order at all. And, in short, while a cer¬ 
tain amount of order exists in the world, it would seem that 
the world is not so orderly as it might be, and, for instance, 
not so much so as a world of pure chance would be. 

But we can never get to the bottom of this question until 
we take account of a highly-important logical principle 5 
which I now proceed to enounce. This principle is that 
any plurality or lot of objects whatever have some character 
in common (no matter how insignificant) which is peculiar 
to them and not shared by anything else. The word 
“ character ” here is taken in such a sense as to include 
negative characters, such as incivility, inequality, etc., as 
well as their positives, civility, equality, etc. To prove the 
theorem, I will show what character any two things, A and 
B, have in common, not shared by anything else. The 
things, A and B, are each distinguished from all other 
things by the possession of certain characters which may be 
named A-ness and B-ness. Corresponding to these posi- 

5 This principle was, I believe, first stated by Mr. De Morgan. 


THE ORDER OF NATURE 


ii3 


tive characters, are the negative characters un-A-ness, which 
is possessed by everything except A, and un-B-ness, which 
is possessed by everything except B. These two characters 
are united in everything except A and B; and this union 
of the characters un-A-ness and un-B-ness makes a com¬ 
pound character which may be termed A-B-lessness. This 
is not possessed by either A or B, but it is possessed by 
everything else. This character, like every other, has its 
corresponding negative un-A-B-lessness, and this last is the 
character possessed by both A and B, and by nothing else. 
It is obvious that what has thus been shown true of two 
things is mutatis mutandis, true of any number of things. 
Q. E. D. 

In any world whatever, then, there must be a character 
peculiar to each possible group of objects. If, as a matter 
of nomenclature, characters peculiar to the same group be 
regarded as only different aspects of the same character, 
then we may say that there will be precisely one character 
for each possible group of objects. Thus, suppose a world 
to contain five things, a, P, 7, 8 , e. Then it will have a 
separate character for each of the 31 groups (with non¬ 
existence making up 32 or 2 5 ) shown in the following table: 


Table II. 



ap 

apy 

aPyd 

a 

a7 

aPd 

apye 

P 

a8 

aPe 

aPde 

y 

ae 

ay d 

ay de 

d 

Py 

aye 

pyde 

e 

ps 

ade 



Pe 

(iyt> 



yd 

Pye 



ye 

pde 



de 

y de 



apyde 


CHANCE AND LOGIC 


114 

This shows that a contradiction is involved in the very 
idea 6 of a chance-world, for in a world of 32 things, in¬ 
stead of there being only 3 s or 243 characters, as we have 
seen that the notion of a chance-world requires, there would, 
in fact, be no less than 2 32 , or 4,294,967,296 characters, 
which would not be all independent, but would have all 
possible relations with one another. 

We further see that so long as we regard characters 
abstractly, without regard to their relative importance, etc., 
there is no possibility of a more or less degree of orderli¬ 
ness in the world, the whole system of relationship between 
the different characters being given by mere logic; that is, 
being implied in those facts which are tacitly admitted as 
soon as we admit that there is any such thing as reasoning. 

In order to descend from this abstract point of view, it 
is requisite to consider the characters of things as relative 
to the perceptions and active powers of living beings. In¬ 
stead, then, of attempting to imagine a world in which there 
should be no uniformities, let us suppose one in which none 
of the uniformities should have reference to characters 
interesting or important to us. In the first place, there 
would be nothing to puzzle us in such a world. The small 
number of qualities which would directly meet the senses 
would be the ones which would afford the key to every¬ 
thing which could possibly interest us. The whole uni¬ 
verse would have such an air of system and perfect regu¬ 
larity that there would be nothing to ask. In the next 
place, no action of ours, and no event of Nature, would have 
important consequences in such a world. We should be 

6 Not in every idea but only in the one so formulated. 


THE ORDER OF NATURE 115 

perfectly free from all responsibility, and there would be 
nothing to do but to enjoy or suffer whatever happened to 
come along. Thus there would be nothing to stimulate or 
develop either the mind or the will, and we consequently 
should neither act nor think. We should have no memory, 
because that depends on a law of our organization. Even 
if we had any senses, we should be situated toward such a 
world precisely as inanimate objects are toward the present 
one, provided we suppose that these objects have an abso¬ 
lutely transitory and instantaneous consciousness without 
memory — a supposition which is a mere mode of speech, 
for that would be no consciousness at all. We may, there¬ 
fore, say that a world of chance is simply our actual world 
viewed from the standpoint of an animal at the very van¬ 
ishing-point of intelligence. The actual world is almost a 
chance-medley to the mind of a polyp. The interest which 
the uniformities of Nature have for an animal measures 
his place in the scale of intelligence. 

Thus, nothing can be made out from the orderliness of 
Nature in regard to the existence of a God, unless it be 
maintained that the existence of a finite mind proves the 
existence of an infinite one. 


hi 

In the last of these papers we examined the nature of 
inductive or synthetic reasoning. W r e found it to be a 
process of sampling. A number of specimens of a class 
are taken, not by selection within that class, but at random. 
These specimens will agree in a great number of respects. 
If, now, it were likely that a second lot would agree with 


n6 CHANCE AND LOGIC 

the first in the majority of these respects, we might base 
on this consideration an inference in regard to any one of 
these characters. But such an inference would neither be 
of the nature of induction, nor would it (except in special 
cases) be valid, because the vast majority of points of 
agreement in the first sample drawn would generally be 
entirely accidental, as well as insignificant. To illustrate 
this, I take the ages at death of the first five poets given in 
Wheeler’s Biographical Dictionary . They are: 

Aagard, 48. 

Abeille, 70. 

Abulola, 84. 

Abunowas, 48. 

Accords, 45. 

These five ages have the following characters in common: 

1. The difference of the two digits composing the num¬ 
ber, divided by three, leaves a remainder of one. 

2. The first digit raised to the power indicated by the 
second, and divided by three, leaves a remainder of one. 

3. The sum of the prime factors of each age, including 
one, is divisible by three. 

It is easy to see that the number of accidental agree¬ 
ments of this sort would be quite endless. But suppose 
that, instead of considering a character because of its prev¬ 
alence in the sample, we designate a character before 
taking the sample, selecting it for its importance, obvious¬ 
ness, or other point of interest. Then two considerable 
samoles drawn at random are extremely likely to agree 


THE ORDER OF NATURE 


117 


approximately in regard to the proportion of occurrences 
of a character so chosen. The inference that a previously 
designated character has nearly the same frequency of 
occurrence in the whole of a class that it has in a sample 
drawn at random out of that class is induction . If the char¬ 
acter be not previously designated, then a sample in which 
it is found to be prevalent can only serve to suggest that 
it may he prevalent in the whole class. We may consider 
this surmise as an inference if we please — an inference 
of possibility; but a second sample must be drawn to test 
the question of whether the character actually is prevalent. 
Instead of designating beforehand a single character in 
reference to which we will examine a sample, we may desig¬ 
nate two, and use the same sample to determine the relative 
frequencies of both. This will be making two inductive 
inferences at once; and, of course, we are less certain that 
both will yield correct conclusions than we should be that 
either separately would do so. What is true of two char¬ 
acters is true of any limited number. Now, the number 
of characters which have any considerable interest for us 
in reference to any class of objects is more moderate than 
might be supposed. As we shall be sure to examine any 
sample with reference to these characters, they may be 
regarded not exactly as predesignated, but as predeter¬ 
mined (which amounts to the same thing); and we may 
infer that the sample represents the class in all these re¬ 
spects if we please, remembering only that this is not so 
secure an inference as if the particular quality to be looked 
for had been fixed upon beforehand. 

The demonstration of this theory of induction rests upon 


118 


CHANCE AND LOGIC 


principles and follows methods which are accepted by all 
those who display in other matters the particular knowledge 
and force of mind which qualify them to judge of this. The 
theory itself, however, quite unaccountably seems never to 
have occurred to any of the writers who have undertaken 
to explain synthetic reasoning. The most widely-spread 
opinion in the matter is one which was much promoted by 
Mr. John Stuart Mill — namely, that induction depends 
for its validity upon the uniformity of Nature — that is, 
on the principle that what happens once will, under a suf¬ 
ficient degree of similarity of circumstances, happen again 
as often as the same circumstances recur. The application 
is this: The fact that different things belong to the same 
class constitutes the similarity of circumstances, and the 
induction is good, provided this similarity is “ sufficient.” 
What happens once is, that a number of these things are 
found to have a certain character; what may be expected, 
then, to happen again as often as the circumstances recur 
consists in this, that all things belonging to the same class 
should have the same character. 

This analysis of induction has, I venture to think, va¬ 
rious imperfections, to some of which it may be useful to 
call attention. In the first place, when I put my hand in 
a bag and draw out a handful of beans, and, finding three- 
quarters of them black, infer that about three-quarters of 
all in the bag are black, my inference is obviously of the 
same kind as if I had found any larger proportion, or the 
whole, of the sample black, and had assumed that it rep¬ 
resented in that respect the rest of the contents of the bag. 
But the analysis in question hardly seems adapted to the 


THE ORDER OF NATURE 


119 


explanation of this proportionate induction, where the con¬ 
clusion, instead of being that a certain event uniformly 
happens under certain circumstances, is precisely that it 
does not uniformly occur, but only happens in a certain 
proportion of cases. It is true that the whole sample may 
be regarded as a single object, and the inference may be 
brought under the formula proposed by considering the 
conclusion to be that any similar sample will show a similar 
proportion among its constituents. But this is to treat the 
induction as if it rested on a single instance, which gives 
a very false idea of its probability. 

In the second place, if the uniformity of Nature were the 
sole warrant of induction, we should have no right to draw 
one in regard to a character whose constancy we knew 
nothing about. Accordingly, Mr. Mill says that, though 
none but white swans were known to Europeans for thou¬ 
sands of years, yet the inference that all swans w^ere white 
was “ not a good induction,” because it was not known 
that color was a usual generic character (it, in fact, not 
being so by any means). But it is mathematically demon¬ 
strable that an inductive inference may have as high a de¬ 
gree of probability as you please independent of any ante¬ 
cedent knowledge of the constancy of the character inferred. 
Before it was known that color is not usually a character 
of genera, there was certainly a considerable probability 
that all swans were white. But the further study of the 
genera of animals led to the induction of their non-uni¬ 
formity in regard to color. A deductive application of 
this general proposition would have gone far to overcome 
the probability of the universal whiteness of swans before 


120 


CHANCE AND LOGIC 


the black species was discovered. When we do know any¬ 
thing in regard to the general constancy or inconstancy of 
a character, the application of that general knowledge to 
the particular class to which any induction relates, though 
it serves to increase or diminish the force of the induction, 
is, like every application of general knowledge to particular 
cases, deductive in its nature and not inductive. 

In the third place, to say that inductions are true because 
similar events happen in similar circumstances — or, what 
is the same thing, because objects similar in some respects 
are likely to be similar in others — is to overlook those 
conditions which really are essential to the validity of in¬ 
ductions. When we take all the characters into account, 
any pair of objects resemble one another in just as many 
particulars as any other pair. If we limit ourselves to such 
characters as have for us any importance, interest, or 
obviousness, then a synthetic conclusion may be drawn, 
but only on condition that the specimens by which we 
judge have been taken at random from the class in regard 
to which we are to form a judgment, and not selected as 
belonging to any sub-class. The induction only has its full 
force when the character concerned has been designated 
before examining the sample. These are the essentials of 
induction, and they are not recognized in attributing the 
validity of induction to the uniformity of Nature. The 
explanation of induction by the doctrine of probabilities, 
given in the last of these papers, is not a mere metaphysical 
formula, but is one from which all the rules of synthetic 
reasoning can be deduced systematically and with mathe¬ 
matical cogency. But the account of the matter by a prin- 


THE ORDER OF NATURE 


I 21 


ciple of Nature, even if it were in other respects satisfactory, 
presents the fatal disadvantage of leaving us quite as much 
afloat as before in regard to the proper method of induc¬ 
tion. It does not surprise me, therefore, that those who 
adopt this theory have given erroneous rules for the con¬ 
duct of reasoning, nor that the greater number of examples 
put forward by Mr. Mill in his first edition, as models of 
what inductions should be, proved in the light of further 
scientific progress so particularly unfortunate that they had 
to be replaced by others in later editions. One would have 
supposed that Mr. Mill might have based an induction on 
this circumstance, especially as it is his avowed principle 
that, if the conclusion of an induction turns out false, it 
cannot have been a good induction. Nevertheless, neither 
he nor any of his scholars seem to have been led to suspect, 
in the least, the perfect solidity of the framework which he 
devised for securely supporting the mind in its passage 
from the known to the unknown, although at its first trial 
it did not answer quite so well as had been expected. 

rv 

When we have drawn any statistical induction — such, 
for instance, as that one-half of all births are of male chil¬ 
dren— it is always possible to discover, by investigation 
sufficiently prolonged, a class of which the same predicate 
may be affirmed universally; to find out, for instance, what 
sort of births are of male children. The truth of this prin¬ 
ciple follows immediately from the theorem that there is a 
character peculiar to every possible group of objects. The 


1 2 % 


CHANCE AND LOGIC 


form in which the principle is usually stated is, that every 
event must have a cause. 

But, though there exists a cause for every event, and 
that of a kind which is capable of being discovered, yet if 
there be nothing to guide us to the discovery; if we have 
to hunt among all the events in the world without any 
scent; if, for instance, the sex of a child might equally be 
supposed to depend on the configuration of the planets, on 
what was going on at the antipodes, or on anything else — 
then the discovery would have no chance of ever getting 
made. 

That we ever do discover the precise causes of things, 
that any induction whatever is absolutely without excep¬ 
tion, is what we have no right to assume. On the contrary, 
it is an easy corollary, from the theorem just referred to, 
that every empirical rule has an exception. 7 But there are 
certain of our inductions which present an approach to 
universality so extraordinary that, even if we are to sup¬ 
pose that they are not strictly universal truths, we cannot 
possibly think that they have been reached merely by 
accident. The most remarkable laws of this kind are those 
of time and space. With reference to space, Bishop 
Berkeley first showed, in a very conclusive manner, that 
it was not a thing seen , but a thing inferred. Berkeley 
chiefly insists on the impossibility of directly seeing the 
third dimension of space, since the retina of the eye is a 
surface. But, in point of fact, the retina is not even a 
surface; it is a conglomeration of nerve-needles directed 

7 [Note that this corollary is itself a theoretical inference and not an 
empirical rule.] 


THE ORDER OF NATURE 


123 


toward the light and having only their extreme points sen¬ 
sitive, these points lying at considerable distances from one 
another compared with their areas. Now, of these points, 
certainly the excitation of no one singly can produce the 
perception of a surface, and consequently not the aggregate 
of all the sensations can amount to this. But certain rela¬ 
tions subsist between the excitations of different nerve- 
points, and these constitute the premises upon which the 
hypothesis of space is founded, and from which it is in¬ 
ferred. That space is not immediately perceived is now 
universally admitted; and a mediate cognition is what is 
called an inference, and is subject to the criticism of logic. 
But what are we to say to the fact of every chicken as soon 
as it is hatched solving a problem whose data are of a com¬ 
plexity sufficient to try the greatest mathematical powers? 
It would be insane to deny that the tendency to light upon 
the conception of space is inborn in the mind of the chicken 
and of every animal. The same thing is equally true of 
time. That time is not directly perceived is evident, since 
no lapse of time is present, and we only perceive what is 
present. That, not having the idea of time, we should 
never be able to perceive the flow in our sensations without 
some particular aptitude for it, will probably also be ad¬ 
mitted. The idea of force — at least, in its rudiments — 
is another conception so early arrived at, and found in 
animals so low in the scale of intelligence, that it must be 
supposed innate. But the innateness of an idea admits 
of degree, for it consists in the tendency of that idea to 
present itself to the mind. Some ideas, like that of space, 
do so present themselves irresistibly at the very dawn of 


124 


CHANCE AND LOGIC 


intelligence, and take possession of the mind on small prov¬ 
ocation, while of other conceptions we are prepossessed, 
indeed, but not so strongly, down a scale which is greatly 
extended. The tendency to personify every thing, and to 
attribute human characters to it, may be said to be innate; 
but it is a tendency which is very soon overcome by civilized 
man in regard to the greater part of the objects about him. 
Take such a conception as that of gravitation varying in¬ 
versely as the square of the distance. It is a very simple 
law. But to say that it is simple is merely to say that it 
is one which the mind is particularly adapted to apprehend 
with facility. Suppose the idea of a quantity multiplied 
into another had been no more easy to the mind than that 
of a quantity raised to the power indicated by itself — 
should we ever have discovered the law of the solar system? 

It seems incontestable, therefore, that the mind of man 
is strongly adapted to the comprehension of the world; at 
least, so far as this goes, that certain conceptions, highly 
important for such a comprehension, naturally arise in his 
mind; and, without such a tendency, the mind could never 
have had any development at all. 

How are we to explain this adaptation? The great 
utility and indispensableness of the conceptions of time, 
space, and force, even to the lowest intelligence, are such 
as to suggest that they are the results of natural selection. 
Without something like geometrical, kinetical, and mechani¬ 
cal conceptions, no animal could seize his food or do any¬ 
thing which might be necessary for the preservation of the 
species. He might, it is true, be provided with an instinct 
which would generally have the same effect; that is to say, 


THE ORDER OF NATURE 


125 


he might have conceptions different from those of time, 
space, and force, but which coincided with them in regard 
to the ordinary cases of the animaPs experience. But, as 
that animal would have an immense advantage in the 
struggle for life whose mechanical conceptions did not break 
down in a novel situation (such as development must bring 
about), there would be a constant selection in favor of 
more and more correct ideas of these matters. Thus would 
be attained the knowledge of that fundamental law upon 
which all science rolls; namely, that forces depend upon 
relations of time, space, and mass. When this idea was 
once sufficiently clear, it would require no more than a 
comprehensible degree of genius to discover the exact na¬ 
ture of these relations. Such an hypothesis naturally sug¬ 
gests itself, but it must be admitted that it does not seem 
sufficient to account for the extraordinary accuracy with 
which these conceptions apply to the phenomena of Nature, 
and it is probable that there is some secret here which 
remains to be discovered. 


v 

Some important questions of logic depend upon whether 
we are to consider the material universe as of limited ex¬ 
tent and finite age, or quite boundless in space and in time. 
In the former case, it is conceivable that a general plan 
or design embracing the whole universe should be discov¬ 
ered, and it would be proper to be on the alert for some 
traces of such a unity. In the latter case, since the pro¬ 
portion of the world of which we can have any experience 
is less than the smallest assignable fraction, it follows that 


CHANCE AND LOGIC 


126 

we never could discover any pattern in the universe except 
a repeating one; any design embracing the whole would be 
beyond our powers to discern, and beyond the united powers 
of all intellects during all time. Now, what is absolutely 
incapable of being known is, as we have seen in a former 
paper, not real at all. An absolutely incognizable existence 
is a nonsensical phrase. If, therefore, the universe is infinite, 
the attempt to find in it any design embracing it as a whole 
is futile, and involves a false way of looking at the subject. 
If the universe never had any beginning, and if in space 
world stretches beyond world without limit, there is no 
whole of material things, and consequently no general char¬ 
acter to the universe, and no need or possibility of any 
governor for it. But if there was a time before which 
absolutely no matter existed, if there are certain absolute 
bounds to the region of things outside of which there is a 
mere void, then we naturally seek for an explanation of it, 
and, since we cannot look for it among material things, 
the hypothesis of a great disembodied animal, the creator 
and governor of the world, is natural enough. 

The actual state of the evidence as to the limitation of 
the universe is as follows: As to time, we find on our earth 
a constant progress of development since the planet was a 
red-hot ball; the solar system seems to have resulted from 
the condensation of a nebula, and the process appears to 
be still going on. We sometimes see stars (presumably 
with systems of worlds) destroyed and apparently resolved 
back into the nebulous condition, but we have no evidence 
of any existence of the world previous to the nebulous stage 
from which it seems to have been evolved. All this rather 


THE ORDER OF NATURE 


127 


favors the idea of a beginning than otherwise. As for 
limits in space, we cannot be sure that we see anything 
outside of the system of the Milky Way. Minds of theo¬ 
logical predilections have therefore no need of distorting the 
facts to reconcile them with their views. 

But the only scientific presumption is, that the unknown 
parts of space and time are like the known parts, occupied; 
that, as w r e see cycles of life and death in all development 
which we can trace out to the end, the same holds good in 
regard to solar systems; that as enormous distances lie be¬ 
tween the different planets of our solar system, relatively 
to their diameters, and as still more enormous distances lie 
between our system relatively to its diameter and other 
systems, so it may be supposed that other galactic clusters 
exist so remote from ours as not to be recognized as such 
with certainty. I do not say that these are strong induc¬ 
tions; I only say that they are the presumptions which, 
in our ignorance of the facts, should be preferred to hy¬ 
potheses which involve conceptions of things and occur¬ 
rences totally different in their character from any of which 
we have had any experience, such as disembodied spirits, 
the creation of matter, infringements of the laws of me¬ 
chanics, etc. 

The universe ought to be presumed too vast to have any 
character. When it is claimed that the arrangements of 
Nature are benevolent, or just, or wise, or of any other 
peculiar kind, we ought to be prejudiced against such 
opinions, as being the offspring of an ill-founded notion 
of the finitude of the world. And examination has hitherto 
shown that such beneficences, justice, etc., are of a most 
limited kind — limited in degree and limited in range. 


CHANCE AND LOGIC 


128 

In like manner, if any one claims to have discovered a 
plan in the structure of organized beings, or a scheme in 
their classification, or a regular arrangement among natural 
objects, or a system of proportionality in the human form, 
or an order of development, or a correspondence between 
conjunctions of the planets and human events, or a signifi¬ 
cance in numbers, or a key to dreams, the first thing we 
have to ask is whether such relations are susceptible of 
explanation on mechanical principles, and if not they should 
be looked upon with disfavor as having already a strong 
presumption against them; and examination has generally 
exploded all such theories. 

There are minds to whom every prejudice, every pre¬ 
sumption, seems unfair. It is easy to say what minds these 
are. They are those who never have known what it is to 
draw a well-grounded induction, and who imagine that 
other people’s knowledge is as nebulous as their own. That 
all science rolls upon presumption (not of a formal but of 
a real kind) is no argument with them, because they can¬ 
not imagine that there is anything solid in human knowl¬ 
edge. These are the people who waste their time and 
money upon perpetual motions and other such rubbish. 

But there are better minds who take up mystical theories 
(by which I mean all those which have no possibility of 
being mechanically explained). These are persons who are 
strongly prejudiced in favor of such theories. We all have 
natural tendencies to believe in such things; our education 
often strengthens this tendency; and the result is, that to 
many minds nothing seems so antecedently probable as 
a theory of this kind. Such persons find evidence enough 


THE ORDER OF NATURE 


129 


in favor of their views, and in the absence of any recognized 
logic of induction they cannot be driven from their belief. 

But to the mind of a physicist there ought to be a strong 
presumption against every mystical theory; and, therefore, 
it seems to me that those scientific men who have sought 
to make out that science was not hostile to theology have 
not been so clear-sighted as their opponents. 

It would be extravagant to say that science can at present 
disprove religion; but it does seem to me that the spirit of 
science is hostile to any religion except such a one as that 
of M. Vacherot. Our appointed teachers inform us that 
Buddhism is a miserable and atheistical faith, shorn of the 
most glorious and needful attributes of a religion; that its 
priests can be of no use to agriculture by praying for rain, 
nor to war by commanding the sun to stand still. We also 
hear the remonstances of those who warn us that to shake 
the general belief in the living God would be to shake the 
general morals, public and private. This, too, must be ad¬ 
mitted; such a revolution of thought could no more be 
accomplished without waste and desolation than a planta¬ 
tion of trees could be transferred to new ground, however 
wholesome in itself, without all of them .languishing for a 
time, and many of them dying. Nor is it, by-the-way, a 
thing to be presumed that a man would have taken part 
in a movement having a possible atheistical issue without 
having taken serious and adequate counsel in regard to that 
responsibility. But, let the consequences of such a belief 
be as dire as they may, one thing is certain: that the state 
of the facts, whatever it may be, will surely get found out, 
and no human prudence can long arrest the triumphal car 


130 


CHANCE AND LOGIC 


of truth — no, not if the discovery were such as to drive 
every individual of our race to suicide! 

But it would be folly to suppose that any metaphysical 
theory in regard to the mode of being of the perfect is to 
destroy that aspiration toward the perfect which constitutes 
the essence of religion. It is true that, if the priests of 
any particular form of religion succeed in making it gen¬ 
erally believed that religion cannot exist without the accept¬ 
ance of certain formulas, or if they succeed in so inter¬ 
weaving certain dogmas with the popular religion that the 
people can see no essential analogy between a religion 
which accepts these points of faith and one which rejects 
them, the result may very well be to render thpse who can¬ 
not believe these things irreligious. Nor can we ever hope 
that any body of priests should consider themselves more 
teachers of religion in general than of the particular system 
of theology advocated by their own party. But no man 
need be excluded from participation in the common feelings, 
nor from so much of the public expression of them as is 
open to all the laity, by the unphilosophical narrowness of 
those who guard the mysteries of worship. Am I to be 
prevented from joining in that common joy at the revela¬ 
tion of enlightened principles of religion, which we celebrate 
at Easter and Christmas, because I think that certain scien¬ 
tific, logical, and metaphysical ideas which have been mixed 
up with these principles are untenable? No; to do so 
would be to estimate those errors as of more consequence 
than the truth — an opinion which few would admit. 
People who do not believe what are really the fundamental 
principles of Christianity are rare to find, and all but these 
few ought to feel at home in the churches. 


SIXTH PAPER 


DEDUCTION, INDUCTION, AND HYPOTHESIS 1 

I 

The chief business of the logician is to classify arguments; 

******** - 

for all testing clearly depends on classification. The classes 
of the logicians are defined by certain typical forms called 
syllogisms. For example, the syllogism called Barbara is 
as follows: 

S is M; M is P: 

Hence, S is P. 

Or, to put words for letters — 

Enoch and Elijah were men; all men die: 

Hence, Enoch and Elijah must have died. 

The “ is P ” of the logicians stands for any verb, active 
or neuter. It is capable of strict proof (with which, how¬ 
ever, I will not trouble‘the reader) that all arguments 
whatever can be put into this form; but only under the 
condition that the is shall mean “ is for the purposes of the 
argument ” or “ is represented by.” Thus, an induction 
will appear in this form something like this: 

These beans are two-thirds white; 

But, the beans in this bag are (represented by) these 

♦ 

beans; 

1 Popular Science Monthly, August, 1878. 


132 


CHANCE AND LOGIC 


The beans in the bag are two-thirds white. 

But, because all inference may be reduced in some way 
to Barbara, it does not follow that this is the most appro¬ 
priate form in which to represent every kind of inference. 
On the contrary, to show the distinctive characters of dif¬ 
ferent sorts of inference, they must clearly be exhibited in 
different forms peculiar to each. Barbara particularly 
typifies deductive reasoning; and so long as the is is taken 
literally, no inductive reasoning can be put into this form. 
Barbara is, in fact, nothing but the application of a rule. 
The so-called major premise lays down this rule; as, for 
example, All men are mortal. The other or minor premise 
states a case under the rule; as, Enoch was a man. The 
conclusion applies the rule to the case and states the result: 
Enoch is mortal. All deduction is of this character; it is 
merely the application of general rules to particular cases. 
Sometimes this is not very evident, as in the following: 

All quadrangles are figures, 

But no triangle is a quadrangle; 

Therefore, some figures are not triangles. 

But here the reasoning is really this: 

Rule. — Every quadrangle is other than a triangle. 

Case. — Some figures are quadrangles. 

Result . — Some figures are not triangles. 

Inductive or synthetic reasoning, being something more 
than the mere application of a general rule to a particular 
case, can never be reduced to this form. 

If, from a bag of beans of which we know that f are 
white, we take one at random, it is a deductive inference 


DEDUCTION, INDUCTION, HYPOTHESIS 133 

that this bean is probably white, the probability being 
We have, in effect, the following syllogism: 

Rule. — The beans in this bag are -§ white. 

Case. — This bean has been drawn in such a way that 
in the long run the relative number of white beans so drawn 
would be equal to the relative number in the bag. 

Result. — This bean has been drawn in such a way that 
in the long run it would turn out white f of the time. 

If instead of drawing one bean we draw a handful at 
random and conclude that about -§ of the handful are prob¬ 
ably white, the reasoning is of the same sort. If, however, 
not knowing what proportion of white beans there are in 
the bag, we draw a handful at random and, finding § of 

N _ 

the beans in the handful white, conclude that about f of 
those in the bag are white, we are rowing up the current 
of deductive sequence, and are concluding a rule from the 
observation of a result in a certain case. This is particu¬ 
larly clear when all the handful turn out one color. The 
induction then is: 

These beans were in this bag_ 

These beans are white- 

.‘.All the beans in the bag were white. 

Which is but an inversion of the deductive 
syllogism. 

Rule. — All the beans in the bag were white.— 

Case. — These beans were in the bag.—- 

Result. — These beans are white. -- 

So that induction is the inference of the rule from the case 
and result. 










134 


CHANCE AND LOGIC 


But this is not the only way of inverting a deductive 
syllogism so as to produce a synthetic inference. Suppose 
I enter a room and there find a number of bags, containing 
different kinds of beans. On the table there is a handful 
of white beans; and, after some searching, I find one of the 
bags contains white beans only. I at once infer as a prob¬ 
ability, or as a fair guess, that this handful was taken out 
of that bag. This sort of inference is called making an 
hypothesis . 2 It is the inference of a case from a rule and 
result . We have, then — 

Deduction. 

Rule. — All the beans from this bag are white. 

Case. — These beans are from this bag. 

.'.Result. — These beans are white. 

Induction. 

Case. — These beans are from this bag. 

Result. — These beans are white. 

.'.Rule. — All the beans from this bag are white. 

Hypothesis. 

Rule. — All the beans from this bag are white. 

Result. — These beans are white. 

.'.Case. — These beans are from this bag. 

We, accordingly, classify all inference as follows: 

Inference. 

•--—■ — ■ — ' - — > 

Deductive or Analytic. Synthetic. 

. ..— ■ ' » . I I J t 

Induction. Hypothesis. 

2 [Later Pierce called it presumptive inference. See Baldwin’s Dic¬ 
tionary art. Probable Inference .] 





DEDUCTION, INDUCTION, HYPOTHESIS 


135 


Induction is where we generalize from a number of cases 
of which something is true, and infer that the same thing 
is true of a whole class. Or, where we find a certain thing 
to be true of a certain proportion of cases and infer that it 
is true of the same proportion of the whole class. Hy¬ 
pothesis is where we find some very curious circumstance, 
which would be explained by the supposition that it was 
a case of a certain general rule, and thereupon adopt that 
supposition. Or, where we find that in certain respects 
two objects have a strong resemblance, and infer that they 
resemble one another strongly in other respects. 

I once landed at a seaport in a Turkish province; and, 
as I was walking up to the house which I was to visit, I 
met a man upon horseback, surrounded by four horsemen 
holding a canopy over his head. As the governor of the 
province was the only personage I could think of who would 
be so greatly honored, I inferred that this was he. This 
was an hypothesis. 

Fossils are found; say, remains like those of fishes, but 
far in the interior of the country. To explain the phe¬ 
nomenon, we suppose the sea once washed over this land. 
This is another hypothesis. 

Numberless documents and monuments refer to a con¬ 
queror called Napoleon Bonaparte. Though we have not 
seen the man, yet we cannot explain what we have seen, 
namely, all these documents and monuments, without sup¬ 
posing that he really existed. Hypothesis again. 

As a general rule, hypothesis is a weak kind of argument. 
It often inclines our judgment so slightly toward its con¬ 
clusion that we cannot say that we believe the latter to 


CHANCE AND LOGIC 


136 

be true; we only surmise that it may be so. But there is no 
difference except one of degree between such an inference 
and that by which we are led to believe that we remember 
the occurrences of yesterday from our feeling as if we did so. 

11 

Besides the way just pointed out of inverting a deductive 
syllogism to produce an induction or hypothesis, there is 
another. If from the truth of a certain premise the truth 
of a certain conclusion would necessarily follow, then from 
the falsity of the conclusion the falsity of the premise would 
follow. Thus, take the following syllogism in Barbara: 

Rule. — All men are mortal. 

Case. — Enoch and Elijah were men. 

.*. Result. — Enoch and Elijah were mortal. 

Now, a person who denies this result may admit the rule, 
and, in that case, he must deny the case. Thus: 

Denial of Result. — Enoch and Elijah were not mortal. 

Rule. — All men are mortal. 

Denial of Case. — Enoch and Elijah were not men. 

This kind of syllogism is called Baroco, which is the typi¬ 
cal mood of the second figure. On the other hand, the 
person who denies the result may admit the case, and in 
that case he must deny the rule. Thus: 

Denial of the Result. — Enoch and Elijah were not 
mortal. 

Case. — Enoch and Elijah were men. 

Denial of the Rule . — Some men are not mortal. 


DEDUCTION, INDUCTION, HYPOTHESIS 


1 37 

This kind of syllogism is called Bocardo, which is the 
typical mood of the third figure. 

Baroco and Bocardo are, of course, deductive syllogisms; 
but of a very peculiar kind. They are called by logicians 
indirect moods, because they need some transformation to 
appear as the application of a rule to a particular case. 
But if, instead of setting out as we have here done with a 
necessary deduction in Barbara, we take a probable deduc¬ 
tion of similar form, the indirect moods which we shall 
obtain will be — 

Corresponding to Baroco, an hypothesis; 
and, Corresponding to Bocardo, an induction. 

For example, let us begin with this probable deduction 
in Barbara: 

Rule. — Most of the beans in this bag are white. 

Case. — This handful of beans are from this bag. 

:. Result. — Probably, most of this handful of beans are 
white. 

Now, deny the result, but accept the rule: 

Denial of Result. — Few beans of this handful are 
white. 

Rule. — Most beans in this bag are white. 

:. Denial of Case. — Probably, these beans were taken 
from another bag. 

This is an hypothetical inference. Next, deny the result, 
but accept the case: 

Denial of Result. — Few beans of this handful are 
white. 

Case. — These beans came from this bag. 



CHANCE AND LOGIC 


138 

Denial of Rule. — Probably, few beans in the bag are 
white. 

This is an induction. 

The relation thus exhibited between synthetic and de¬ 
ductive reasoning is not without its importance. When we 
adopt a certain hypothesis, it is not alone because it will 
explain the observed facts, but also because the contrary 
hypothesis would probably lead to results contrary to those 
observed. So, when we make an induction, it is drawn not 
only because it explains the distribution of characters in 
the sample, but also because a different rule would prob¬ 
ably have led to the sample being other than it is. 

But the advantage of this way of considering the subject 
might easily be overrated. An induction is really the in¬ 
ference of a rule, and to consider it as the denial of a rule 
is an artificial conception, only admissible because, when 
statistical or proportional propositions are considered as 
rules, the denial of a rule is itself a rule. So, an hypothesis 
is really a subsumption of a case under a class and not the 
denial of it, except for this, that to deny a subsumption 
under one class is to admit a subsumption under another. 

Bocardo may be considered as an induction, so timid as 
to lose its amplificative character entirely. Enoch and Eli¬ 
jah are specimens of a certan kind of men. All that kind 
of men are shown by these instances to be immortal. But 
instead of boldly concluding that all very pious men, or all 
men favorites of the Almighty, etc., are immortal, we re¬ 
frain from specifying the description of men, and rest in 
the merely explicative inference that some men are im- 


DEDUCTION, INDUCTION, HYPOTHESIS 


139 


mortal. So Baroco might be considered as a very timid 
hypothesis. Enoch and Elijah are not mortal. Now, we 
might boldly suppose them to be gods or something of that 
sort, but instead of that we limit ourselves to the inference 
that they are of some nature different from that of man. 

But, after all, there is an immense difference between the 
relation of Baroco and Bocardo to Barbara and that of 
Induction and Hypothesis to Deduction. Baroco and Bo¬ 
cardo are based upon the fact that if the truth of a con¬ 
clusion necessarily follows from the truth of a premise, then 
the falsity of the premise follows from the falsity of the 
conclusion. This is always true. It is different when the 
inference is only probable. It by no means follows that, 
because the truth of a certain premise would render the 
truth of a conclusion probable, therefore the falsity of the 
conclusion renders the falsity of the premise probable. At 
least, this is only true, as we have seen in a former paper, 
when the word probable is used in one sense in the ante¬ 
cedent and in another in the consequent. 

hi 

A certain anonymous writing is upon a torn piece of 
paper. It is suspected that the author is a certain person. 
His desk, to which only he has had access, is searched, and 
in it is found a piece of paper, the torn edge of which ex¬ 
actly fits, in all its irregularities, that of the paper in ques¬ 
tion. It is a fair hypothetic inference that the suspected 
man was actually the author. The ground of this inference 
evidently is that two torn pieces of paper are extremely 


140 


CHANCE AND LOGIC 


unlikely to fit together by accident. Therefore, of a great 
number of inferences of this sort, but a very small propor¬ 
tion would be deceptive. The analogy of hypothesis with 
induction is so strong that some logicians have confounded 
them. Hypothesis has been called an induction of charac¬ 
ters. A number of characters belonging to a certain class 
are found in a certain object; whence it is inferred that all 
the characters of that class belong to the object in question. 
This certainly involves the same principle as induction; 
yet in a modified form. In the first place, characters are 
not susceptible of simple enumeration like objects; in the 
next place, characters run in categories. When we make 
an hypothesis like that about the piece of paper, we only 
examine a single line of characters, or perhaps two or three, 
and we take no specimen at all of others. If the hypothesis 
were nothing but an induction, all that we should be justi¬ 
fied in concluding, in the example above, would be that the 
two pieces of paper which matched in such irregularities 
as have been examined would be found to match in other, 
say slighter, irregularities. The inference from the shape 
of the paper to its ownership is precisely what distinguishes 
hypothesis from induction, and makes it a bolder and more 
perilous step. 

The same warnings that have been given against imagin¬ 
ing that induction rests upon the uniformity of Nature 
might be repeated in regard to hypothesis. Here, as there, 
such a theory not only utterly fails to account for the 
validity of the inference, but it also gives rise to methods 
of conducting it which are absolutely vicious. There are, 
no doubt, certain uniformities in Nature, the knowledge of 


DEDUCTION, INDUCTION, HYPOTHESIS 


141 


which will fortify an hypothesis very much. For example, 
we suppose that iron, titanium, and other metals exist in 
the sun, because we find in the solar spectrum many lines 
coincident in position with those which these metals would 
produce; and this hypothesis is greatly strengthened by 
our knowledge of the remarkable distinctiveness of the par¬ 
ticular line of characters observed. But such a fortification 
of hypothesis is of a deductive kind, and hypothesis may 
still be probable when such reenforcement is wanting. 

There is no greater nor more frequent mistake in prac¬ 
tical logic than to suppose that things which resemble one 
another strongly in some respects are any the more likely 
for that to be alike in others. That this is absolutely false, 
admits of rigid demonstration; but, inasmuch as the 
reasoning is somewhat severe and complicated (requiring, 
like all such reasoning, the use of A, B, C, etc., to set it 
forth), the reader would probably find it distasteful, and 
I omit it. An example, however, may illustrate the propo¬ 
sition: The comparative mythologists occupy themselves 
with finding points of resemblance between solar phenom¬ 
ena and the careers of the heroes of all sorts of traditional 
stories; and upon the basis of such resemblances they in¬ 
fer that these heroes are impersonations of the sun. If 
there be anything more in their reasonings, it has never 
been made clear to me. An ingenious logician, to show how 
futile all that is, wrote a little book, in which he pretended 
to prove, in the same manner, that Napoleon Bonaparte 
is only an impersonation of the sun. It was really wonder¬ 
ful to see how many points of resemblance he made out. 
The truth is, that any two things resemble one another 


142 


CHANCE AND LOGIC 


just as strongly as any two others, if recondite resemblances 
are admitted. But, in order that the process of making an 
hypothesis should lead to a probable result, the following 
rules must be followed: 

1. The hypothesis should be distinctly put as a question, 
before making the observations which are to test its truth. 
In other words, we must try to see what the result of pre¬ 
dictions from the hypothesis will be. 

2. The respect in regard to which the resemblances are 
noted must be taken at random. We must not take a par¬ 
ticular kind of predictions for which the hypothesis is known 
to be good. 

3. The failures as well as the successes of the predictions 
must be honestly noted. The whole proceeding must be 
fair and unbiased. 

Some persons fancy that bias and counter-bias are favor¬ 
able to the extraction of truth — that hot and partisan de¬ 
bate is the way to investigate. This is the theory of our 
atrocious legal procedure. But Logic puts its heel upon 
this suggestion. It irrefragably demonstrates that knowl¬ 
edge can only be furthered by the real desire for it, and 
that the methods of obstinacy, of authority, and every mode 
of trying to reach a foregone conclusion, are absolutely of 
no value. These things are proved. The reader is at lib¬ 
erty to think so or not as long as the proof is not set forth, 
or as long as he refrains from examining it. Just so, he 
can preserve, if he likes, his freedom of opinion in regard 
to the propositions of geometry; only, in that case, if he 
takes a fancy to read Euclid, he will do well to skip what¬ 
ever he finds with A, B, C, etc., for, if he reads attentively 


DEDUCTION, INDUCTION, HYPOTHESIS 


*43 


that disagreeable matter, the freedom of his opinion about 
geometry may unhappily be lost forever. 

How many people there are who are incapable of putting 
to their own consciences this question, “ Do I want to know 
how the fact stands, or not? ” 

The rules which have thus far been laid down for in¬ 
duction and hypothesis are such as are absolutely essential. 
There are many other maxims expressing particular con¬ 
trivances for making synthetic inferences strong, which are 
extremely valuable and should not be neglected. Such 
are, for example, Mr. Mill’s four methods. Nevertheless, 
in the total neglect of these, inductions and hypotheses 
may and sometimes do attain the greatest force. 

iv 

Classifications in all cases perfectly satisfactory hardly 
exist. Even in regard to the great distinction between ex¬ 
plicative and ampliative inferences, examples could be found 
which seem to lie upon the border between the two classes, 
and to partake in some respects of the characters of either. 
The same thing is true of the distinction between induction 
and hypothesis. In the main, it is broad and decided. By 
induction, we conclude that facts, similar to observed facts, 
are true in cases not examined. By hypothesis, we con¬ 
clude the existence of a fact quite different from anything 
observed, from which, according to known laws, something 
observed would necessarily result. The former, is reason¬ 
ing from particulars to the general law; the latter, from 
effect to cause. The former classifies, the latter explains. 


1 44 - 


CHANCE AND LOGIC 


It is only in some special cases that there can be more than 
a momentary doubt to which category a given inference 
belongs. One exception is where we observe, not facts sim¬ 
ilar under similar circumstances, but facts different under 
different circumstances — the difference of the former hav¬ 
ing, however, a definite relation to the difference of the 
latter. Such inferences, which are really inductions, some¬ 
times present nevertheless some indubitable resemblances 
to hypotheses. 

Knowing that water expands by heat, we make a number 
of observations of the volume of a constant mass of water 
at different temperatures. The scrutiny of a few of these 
suggests a form of algebraical formula which will approxi¬ 
mately express the relation of the volume to the tempera¬ 
ture. It may be, for instance, that v being the relative 
volume, and t the temperature, a few observations ex¬ 
amined indicate a relation of the form — 

v = i -f- at -f- bt~ -j— ct 3 . 

Upon examining observations at other temperatures taken 
at random, this idea is confirmed; and we draw the induc¬ 
tive conclusion that all observations within the limits of 
temperature from which we have drawn our observations 
could equally be so satisfied. Having once ascertained that 
such a formula is possible, it is a mere affair of arithmetic 
to find the values of a, b, and c, which will make the formula 
satisfy the observations best. This is what physicists call 
an empirical formula, because it rests upon mere induction, 
and is not explained by any hypothesis. 

Such formulae, though very useful as means of describing 


DEDUCTION, INDUCTION, HYPOTHESIS 


145 


in general terms the results of observations, do not take 
any high rank among scientific discoveries. The induction 
which they embody, that expansion by heat (or whatever 
other phenomenon is referred to) takes place in a perfectly 
gradual manner without sudden leaps or inummerable fluc¬ 
tuations, although really important, attracts no attention, 
because it is what we naturally anticipate. But the defects 
of such expressions are very serious. In the first place, as 
long as the observations are subject to error, as all observa¬ 
tions are, the formula cannot be expected to satisfy the 
observations exactly. But the discrepancies cannot be due 
solely to the errors of the observations, but must be partly 
owing to the error of the formula which has been deducted 
from erroneous observations. Moreover, we have no right 
to suppose that the real facts, if they could be had free 
from error, could be expressed by such a formula at all. 
They might, perhaps, be expressed by a similar formula 
with an infinite number of terms; but of what use would 
that be to us, since it would require an infinite number of 
coefficients to be written down? When one quantity varies 
with another, if the corresponding values are exactly known, 
it is a mere matter of mathematical ingenuity to find some 
way of expressing their relation in a simple manner. If 
one quantity is of one kind — say, a specific gravity — and 
the other of another kind — say, a temperature — we do 
not desire to find an expression for their relation which is 

v 

wholly free from numerical constants, since if it were free 
from them when, say, specific gravity as compared with 
water, and temperature as expressed by the Centigrade ther¬ 
mometer, were in question, numbers would have to be in- 


146 CHANCE AND LOGIC 

troduced when the scales of measurement were changed. 
We may, however, and do desire to find formulas expressing 
the relations of physical phenomena which shall contain 
no more arbitrary numbers than changes in the scales of 
measurement might require. 

When a formula of this kind is discovered, it is no longer 
called an empirical formula, but a law of Nature; and is 
sooner or later made the basis of an hypothesis which is 
to explain it. These simple formulae are not usually, if 
ever, exactly true, but they are none the less important for 
that; and the great triumph of the hypothesis comes when 
it explains not only the formula, but also the deviations 
from the formula. In the current language of the physi¬ 
cists, an hypothesis of this importance is called a theory, 
while the term hypothesis is restricted to suggestions which 
have little evidence in their favor. There is some justice 
in the contempt which clings to the word hypothesis. To 
think that we can strike out of our own minds a true pre¬ 
conception of how Nature acts, in a vain fancy. As Lord 
Bacon well says: “ The subtlety of Nature far exceeds the 
subtlety of sense and intellect: so that these fine medita¬ 
tions, and speculations, and reasonings of men are a sort 
of insanity, only there is no one at hand to remark it.” 
The successful theories are not pure guesses, but are guided 
by reasons. 

The kinetical theory of gases is a good example of this. 
This theory is intended to explain certain simple formulae, 
the chief of which is called the law of Boyle. It is, that if 
air or any other gas be placed in a cylinder with a piston, 
and if its volume be measured under the pressure of the 


DEDUCTION, INDUCTION, HYPOTHESIS 


1 47 


atmosphere, say fifteen pounds on the square inch, and if 
then another fifteen pounds per square inch be placed on 
the piston, the gas will be compressed to one-half its bulk, 
and in similar inverse ratio for other pressures. The 
hypothesis which has been adopted to account for this law 
is that the molecules of a gas are small, solid particles at 
great distances from each other (relatively to their dimen¬ 
sions), and moving with great velocity, without sensible 
attractions or repulsions, until they happen to approach 
one another very closely. Admit this, and it follows that 
when a gas is under pressure what prevents it from collaps¬ 
ing is not the incompressibility of the separate mole¬ 
cules, which are under no pressure at all, since they do not 
touch, but the pounding of the molecules against the piston. 
The more the piston falls, and the more the gas is com¬ 
pressed, the nearer together the molecules will be; the 
greater number there will be at any moment within a given 
distance of the piston, the shorter the distance which any 
one will go before its course is changed by the influence of 
another, the greater number of new courses of each in a 
given time, and the oftener each, within a given distance 
of the piston, will strike it. This explains Boyle’s law. The 
law is not exact; but the hypothesis does not lead us to it 
exactly. For, in the first place, if the molecules are large, 
they will strike each other oftener when their mean dis¬ 
tances are diminished, and will consequently strike the 
piston oftener, and will produce more pressure upon it. On 
the other hand, if the molecules have an attraction for one 
another, they will remain for a sensible time within one 
another’s influence, and consequently they will not strike 


148 


CHANCE AND LOGIC 


the wall so often as they otherwise would, and the pressure 
will be less increased by compression. 

When the kinetical theory of gases was first proposed by 
Daniel Bernoulli, in 1738, it rested only on the law of 
Boyle, and was therefore pure hypothesis. It was ac¬ 
cordingly quite naturally and deservedly neglected. But, 
at present, the theory presents quite another aspect; for, 
not to speak of the considerable number of observed facts 
of different kinds with which it has been brought into re¬ 
lation, it is supported by the mechanical theory of heat. 
That bringing together bodies which attract one another, or 
separating bodies which repel one another, when sensible 
motion is not produced nor destroyed, is always accompanied 
by the evolution of heat, is little more than an induction. 
Now, it has been shown by experiment that, when a gas is 
allowed to expand without doing work, a very small amount 
of heat disappears. This proves that the particles of the 
gas attract one another slightly, and but very slightly. It 
follows that, when a gas is under pressure, what prevents 
it from collapsing is not any repulsion between the parti¬ 
cles, since there is none. Now, there are only two modes 
of force known to us, force of position or attractions and 
repulsions, and force of motion. Since, therefore, it is not 
the force of position which gives a gas its expansive force, 
it must be the force of motion. In this point of view, the 
kinetical theory of gases appears as a deduction from the 
mechanical theory of heat. It is to be observed, however, 
that it supposes the same law of mechanics (that there are 
only those two modes of force) which holds in regard to 
bodies such as we can see and examine, to hold also for 



DEDUCTION, INDUCTION, HYPOTHESIS 


H9 


what are very different, the molecules of bodies. Such a 
supposition has but a slender support from induction. Our 
belief in it is greatly strengthened by its connection with the 
law of Boyle, and it is, therefore, to be considered as an 
hypothetical inference. Yet it must be admitted that the 
kinetical theory of gases would deserve little credence if it 
had not been connected with the principles of mechanics. 

The great difference between induction and hypothesis is, 
that the former infers the existence of phenomena such as 
we have observed in cases which are similar, while hypothe¬ 
sis supposes something of a different kind from what we 
have directly observed, and frequently something which 
it would be impossible for us to observe directly. Accord¬ 
ingly, when we stretch an induction quite beyond the limits 
of our observation, the inference partakes of the nature of 
hypothesis. It would be absurd to say that we have no 
inductive warrant for a generalization extending a little 
beyond the limits of experience, and there is no line to be 
drawn beyond which we cannot push our inference; only 
it becomes weaker the further it is pushed. Yet, if an in¬ 
duction be pushed very far, we cannot give it much credence 
unless we find that such an extension explains some fact 
which we can and do observe. Here, then, we have a kind 
of mixture of induction and hypothesis supporting one an¬ 
other; and of this kind are most of the theories of physics. 


CHANCE AND LOGIC 


150 


V 

That synthetic inferences may be divided into induction 
and hypothesis in the manner here proposed, 5 admits of no 
question. The utility and value of the distinction are to 
be tested by their applications. 

Induction is, plainly, a much stronger kind of inference 
than hypothesis; and this is the first reason for distinguish¬ 
ing between them. Hypotheses are sometimes regarded as 
provisional resorts, which in the progress of science are to 
be replaced by inductions. But this is a false view of the 
subject. Hypothetic reasoning infers very frequently a fact 
not capable of direct observation. It is an hypothesis that 
Napoleon Bonaparte once existed. How is that hypothesis 
ever to be replaced by an induction? It may be said that 
from the premise that such facts as we have observed are 
as they would be if Napoleon existed, we are to infer by 
induction that all facts that are hereafter to be observed 
will be of the same character. There is no doubt that every 
hypothetic inference may be distorted into the appearance 
of an induction in this w r ay. But the essence of an induc¬ 
tion is that it infers from one set of facts another set of 
similar facts, whereas hypothesis infers from facts of one 
kind to facts of another. Now, the facts which serve as 
grounds for our belief in the historic reality of Napoleon 
are not by any means necessarily the only kind of facts 
which are explained by his existence. It may be that, at 

3 This division was first made in a course of lectures by the author 
before the Lowell Institute, Boston, in 1866, and was printed in the 
Proceedings of the American Academy of Arts and Sciences, for April 9, 
1867. 


DEDUCTION, INDUCTION, HYPOTHESIS 


151 

the time of his career, events were being recorded in some 
way not now dreamed of, that some ingenious creature on 
a neighboring planet was photographing the earth, and that 
these pictures on a sufficiently large scale may some time 
come into our possession, or that some mirror upon a dis¬ 
tant star will, when the light reaches it, reflect the whole 
story back to earth. Never mind how improbable these 
suppositions are; everything which happens is infinitely 
improbable. I am not saying that these things are likely 
to occur, but that some effect of Napoleon’s existence which 
now seems impossible is certain nevertheless to be brought 
about. The hypothesis asserts that such facts, when they 
do occur, will be of a nature to confirm, and not to refute, 
the existence of the man. We have, in the impossibility of 
inductively inferring hypothetical conclusions, a second 
reason for distinguishing between the two kinds of inference. 

A third merit of the distinction is, that it is associated 
with an important psychological or rather physiological 
difference in the mode of apprehending facts. Induction 
infers a rule. Now, the belief of a rule is a habit. That 
a habit is a rule active in us, is evident. That every belief 
is of the nature of a habit, in so far as it is of a general 
character, has been shown in the earlier papers of this 
series. Induction, therefore, is the logical formula which 
expresses the physiological process of formation of a habit. 
Hypothesis substitutes, for a complicated tangle of predi¬ 
cates attached to one subject, a single conception. Now, 
there is a peculiar sensation belonging to the act of thinking 
that each of these predicates inheres in the subject. In 
hypothetic inference this complicated feeling so produced 


152 


CHANCE AND LOGIC 


is replaced by a single feeling of greater intensity, that 
belonging to the act of thinking the hypothetic conclusion. 
Now, when our nervous system is excited in a complicated 
way, there being a relation between the elements of the 
excitation, the result is a single harmonious disturbance 
which I call an emotion. Thus, the various sounds made 
by the instruments of an orchestra strike upon the ear, 
and the result is a peculiar musical emotion, quite distinct 
from the sounds themselves. This emotion is essentially 
the same thing as an hypothetic inference, and every hypo¬ 
thetic inference involves the formation of such an emotion. 
We may say, therefore, that hypothesis produces the sensu¬ 
ous element of thought, and induction the habitual element. 
As for deduction, which adds nothing to the premises, but 
only out of the various facts represented in the premises 
selects one and brings the attention down to it, this may 
be considered as the logical formula for paying attention, 
which is the volitional element of thought, and corresponds 
to nervous discharge in the sphere of physiology. 

Another merit of the distinction between induction and 
hypothesis is, that it leads to a very natural classification 
of the sciences and of the minds which prosecute them. 
What must separate different kinds of scientific men more 
than anything else are the differences of their techniques. 
We cannot expect men who work with books chiefly to 
have much in common with men whose lives are passed in 
laboratories. But, after differences of this kind, the next 
most important are differences in the modes of reasoning. 
Of the natural sciences, we have, first, the classificatory 
sciences, which are purely inductive — systematic botany 


DEDUCTION, INDUCTION, HYPOTHESIS 


153 


and zoology, mineralogy, and chemistry. Then, we have 
the sciences of theory, as above explained — astronomy, 
pure physics, etc. Then, we have sciences of hypothesis — 
geology, biology, etc. 

There are many other advantages of the distinction in 
question which I shall leave the reader to find out by ex¬ 
perience. If he will only take the custom of considering 
whether a given inference belongs to one or other of the 
two forms of synthetic inference given on page 134, I can 
promise him that he will find his advantage in it, in 
various ways. 




PART II 

LOVE AND CHANCE 




< 


LOVE AND CHANCE 

I. THE ARCHITECTURE OF THEORIES 1 

Of the fifty or hundred systems of philosophy that have 
been advanced at different times of the world’s history, 
perhaps the larger number have been, not so much results 
of historical evolution, as happy thoughts which have acci¬ 
dently occurred to their authors. An idea which has been 
found interesting and fruitful has been adopted, developed, 
and forced to yield explanations of all sorts of phenomena. 
The English have been particularly given to this way of 
philosophizing; witness, Hobbes, Hartley, Berkeley, James 
Mill. Nor has it been by any means useless labor; it 
shows us what the true nature and value of the ideas de¬ 
veloped are, and in that way affords serviceable materials 
for philosophy. Just as if a man, being seized with the 
conviction that paper was a good material to make things 
of, were to go to work to build a papier machb house, with 
roof of roofing-paper, foundations of pasteboard, windows 
of paraffined paper, chimneys, bath tubs, locks, etc., all of 
different forms of paper, his experiment would probably 
afford valuable lessons to builders, while it would certainly 
make a detestable house, so those one-idea’d philosophies 
are exceedingly interesting and instructive, and yet are quite 
unsound. 

The remaining systems of philosophy have been of the 
nature of reforms, sometimes amounting to radical revolu¬ 
tions, suggested by certain difficulties which have been found 

1 The Monist, January, 1891. S 

iS7 


i 5 8 


LOVE AND CHANCE 


to beset systems previously in vogue; and such ought cer¬ 
tainly to be in large part the motive of any new theory. 
This is like partially rebuilding a house. The faults that 
have been committed are, first, that the repairs of the 
dilapidations have generally not been sufficiently thorough¬ 
going, and second, that not sufficient pains had been taken 
to bring the additions into deep harmony with the really 
sound parts of the old structure. 

When a man is about to build a house, what a power of 
thinking he has to do, before he can safely break ground! 
With what pains he has to excogitate the precise wants that 
are to be supplied! What a study to ascertain the most 
available and suitable materials, to determine the mode 
of construction to which those materials are best adapted, 
and to answer a hundred such questions! Now without 
riding the metaphor too far, I think we may safely say 
that the studies preliminary to the construction of a great 
theory should be at least as deliberate and thorough as 
those that are preliminary to the building of a dwelling- 
house. 

That systems ought to be constructed architectonically 
has been preached since Kant, but I do not think the full 
import of the maxim has by any means been apprehended. 
What I would recommend is that every person who wishes 
to form an opinion concerning fundamental problems, should 
first of all make a complete survey of human knowledge, 
should take note of all the valuable ideas in each branch of 
science, should observe in just what respect each has been 
successful and where it has failed, in order that in the light 
of the thorough acquaintance so attained of the available 


THE ARCHITECTURE OF THEORIES 


*59 


materials for a philosophical theory and of the nature and 
strength of each, he may proceed to the study of what the 
problem of philosophy consists in, and of the proper way 
of solving it. I must not be understood as endeavoring 
to state fully all that these preparatory studies should em¬ 
brace; on the contrary, I purposely slur over many points, 
in order to give emphasis to one special recommendation, 
namely, to make a systematic study of the conceptions out 
of which a philosophical theory may be built, in order to 
ascertain what place each conception may fitly occupy in 
such a theory, and to what uses it is adapted. 

The adequate treatment of this single point would fill a 
volume, but I shall endeavor to illustrate my meaning by 
glancing at several sciences and indicating conceptions in 
them serviceable for philosophy. As to the results to which 
long studies thus commenced have led me, I shall just give 
a hint at their nature. 

We may begin with dynamics, — field in our day of 
perhaps the grandest conquest human science has ever 
made, — I mean the law of the conservation of energy. 
But let us revert to the first step taken by modern scientific 
thought, — and a great stride it was, — the inauguration of 
dynamics by Galileo. A modern physicist on examining 
Galileo’s works is surprised to find how little experiment 
had to do with the establishment of the foundations of 
mechanics. His principal appeal is to common sense and 
il lume naturale. He always assumes that the true theory 
will be found to be a simple and natural one. And we can 
see why it should indeed be so in dynamics. For instance, 
a body left to its own inertia, moves in a straight line, and 


i6o 


LOVE AND CHANCE 


a straight line appears to us the simplest of curves. In 
itself, no curve is simpler than another. A system of 
straight lines has intersections precisely corresponding to 
those of a system of like parabolas similarly placed, or to 
those of any one of an infinity of systems of curves. But 
the straight line appears to us simple, because, as Euclid 
says, it lies evenly between its extremities; that is, because 
viewed endwise it appears as a point. That is, again, be¬ 
cause light moves in straight lines. Now, light moves in 
straight lines because of the part which the straight line 
plays in the laws of dynamics. Thus it is that our minds 
having been formed under the influence of phenomena 
governed by the laws of mechanics, certain conceptions 
entering into those laws become implanted in our minds, 
so that we readily guess at what the laws are. Without 
such a natural prompting, having to search blindfold for 
a law which would suit the phenomena, our chance of find¬ 
ing it would be as one to infinity. The further physical 
studies depart from phenomena which have directly in¬ 
fluenced the growth of the mind, the less we can expect to 
find the laws which govern them “ simple,” that is, com¬ 
posed of a few conceptions natural to our minds. 

The researches of Galileo, followed up by Huygens and 
others, led to those modern conceptions of Force and Law, 
which have revolutionized the intellectual world. The great 
attention given to mechanics in the seventeenth century 
soon so emphasized these conceptions as to give rise to the 
Mechanical Philosophy, or doctrine that all the phenomena 
of the physical universe are to be explained upon mechani¬ 
cal principles. Newton’s great discovery imparted a new 


THE ARCHITECTURE OF THEORIES 161 

impetus to this tendency. The old notion that heat consists 
in an agitation of corpuscles was now applied to the ex¬ 
planation of the chief properties of gases. The first sugges¬ 
tion in this direction was that the pressure of gases is 
explained by the battering of the particles against the walls 
of the containing vessel, which explained Boyle’s law of the 
compressibility of air. Later, the expansion of gases, Avo- 
gadro’s chemical law, the diffusion and viscosity of gases, 
and the action of Crookes’s radiometer were shown to be 
consequences of the same kinetical theory; but other phe¬ 
nomena, such as the ratio of the specific heat at constant 
volume to that at constant pressure, require additional 
hypotheses, which we have little reason to suppose are 
simple, so that we find ourselves quite afloat. In like 
manner with regard to light. That it consists of vibrations 
was almost proved by the phenomena of diffraction, while 
those of polarization showed the excursions of the particles 
to be perpendicular to the line of propagation; but the 
phenomena of dispersion, etc., require additional hypotheses 
which may be very complicated. Thus, the further prog¬ 
ress of molecular speculation appears quite uncertain. If 
hypotheses are to be tried haphazard, or simply because 
they will suit certain phenomena, it will occupy the mathe¬ 
matical physicists of the world say half a century on the 
average to bring each theory to the test, and since the num¬ 
ber of possible theories may go up into the trillions, only 
one of which can be true, we have little prospect of making 
further solid additions to the subject in our time. When 
we come to atoms, the presumption in favor of a simple law 
seems very slender. There is room for serious doubt 


i6z 


LOVE AND CHANCE 


whether the fundamental laws of mechanics hold good for 
single atoms, and it seems quite likely that they are capable 
of motion in more than three dimensions. 

To find out much more about molecules and atoms, we 
must search out a natural history of laws of nature, which 
may fulfil that function which the presumption in favor 
of simple laws fulfilled in the early days of dynamics, by 
showing us what kind of laws we have to expect and by 
answering such questions as this: Can we with reasonable 
prospect of not wasting time, try the supposition that atoms 
attract one another inversely as the seventh power of their 
distances, or can we not? To suppose universal laws of 
nature capable of being apprehended by the mind and yet 
having no reason for their special forms, but standing in¬ 
explicable and irrational, is hardly a justifiable position. 
Uniformities are precisely the sort of facts that need to be 
accounted for. That a pitched coin should sometimes turn 
up heads and sometimes tails calls for no particular ex¬ 
planation; but if it shows heads every time, we wish to know 
how this result has been brought about. Law is par ex¬ 
cellence the thing that wants a reason. 

Now the only possible way of accounting for the laws of 
nature and for uniformity in general is to suppose them 
results of evolution. This supposes them not to be abso¬ 
lute, not to be obeyed precisely. It makes an element of 
indeterminacy, spontaneity, or absolute chance in nature. 
Just as, when we attempt to verify any physical law, we 
find our observations cannot be precisely satisfied by it, 
and rightly attribute the discrepancy to errors of observa¬ 
tion, so we must suppose far more minute discrepancies to 


THE ARCHITECTURE OF THEORIES 163 

exist owing to the imperfect cogency of the law itself, to a 
certain swerving of the facts from any definite formula. 

Mr. Herbert Spencer wishes to explain evolution upon 
mechanical principles. This is illogical, for four reasons. 
First, because the principle of evolution requires no ex¬ 
traneous cause; since the tendency to growth can be sup¬ 
posed itself to have grown from an infinitesimal germ acci¬ 
dentally started. Second, because law ought more than 
anything else to be supposed a result of evolution. Third, 
because exact law obviously never can produce heterogeneity 
out of homogeneity; and arbitrary heterogeneity is the 
feature of the universe the most manifest and characteristic. 
Fourth, because the law of the conservation of energy is 
equivalent to the proposition that all operations governed 
by mechanical laws are reversible; so that an immediate 
corollary from it is that growth is not explicable by those 
laws, even if they be not violated in the process of growth. 
In short, Spencer is not a philosophical evolutionist, but 
only a half-evolutionist, — or, if you will, only a semi- 
Spencerian. Now philosophy requires thoroughgoing evo¬ 
lutionism or none. 

The theory of Darwin was that evolution had been 
brought about by the action of two factors: first, heredity, 
as a principle making offspring nearly resemble their 
parents, while yet giving room for “ sporting,” or accidental 
variations, — for very slight variations often, for wider ones 
rarely; and, second, the destruction of breeds or races that 
are unable to keep the birth rate up to the death rate. 
This Darwinian principle is plainly capable of great gen¬ 
eralization. Wherever there are large numbers of objects, 


164 


LOVE AND CHANCE 


having a tendency to retain certain characters unaltered, 
this tendency, however, not being absolute but giving room 
for chance variations, then, if the amount of variation is 
absolutely limited in certain directions by the destruction 
of everything which reaches those limits, there will be a 
gradual tendency to change in directions of departure 
from them. Thus, if a million players sit down to bet at 
an even game, since one after another will get ruined, the 
average wealth of those who remain will perpetually in¬ 
crease. Here is indubitably a genuine formula of possible 
evolution, whether its operation accounts for much or little 
in the development of animal and vegetable species. 

The Lamarckian theory also supposes that the develop¬ 
ment of species has taken place by a long series of in¬ 
sensible changes, but it supposes that those changes have 
taken place during the lives of the individuals, in conse¬ 
quence of effort and exercise, and that reproduction plays 
no part in the process except in preserving these modifica¬ 
tions. Thus, the Lamarckian theory only explains the 
development of characters for which individuals strive, while 
the Darwinian theory only explains the production of char¬ 
acters really beneficial to the race, though these may be 
fatal to individuals . 2 But more broadly and philosophically 
conceived, Darwinian evolution is evolution by the opera¬ 
tion of chance, and the destruction of bad results, while 
Lamarckian evolution is evolution by the effect of habit 
and effort. 

A third theory of evolution is that of Mr. Clarence King. 

2 The neo-Darwinian, Weismann, has shown that mortality would 
almost necessarily result from the action of the Darwinian principle. 


THE ARCHITECTURE OF THEORIES 165 

The testimony of monuments and of rocks is that species 
are unmodified or scarcely modified, under ordinary cir¬ 
cumstances, but are rapidly altered after cataclysms or 
rapid geological changes. Under novel circumstances, we 
often see animals and plants sporting excessively in repro¬ 
duction, and sometimes even undergoing transformations 
during individual life, phenomena no doubt due partly to 
the enfeeblement of vitality from the breaking up of hab¬ 
itual modes of life, partly to changed food, partly to direct 
specific influence of the element in which the organism is 
immersed. If evolution has been brought about in this 
way, not only have its single steps not been insensible, as 
both Darwinians and Lamarckians suppose, but they are 
furthermore neither haphazard on the one hand, nor yet 
determined by an inward striving on the other, but on the 
contrary are effects of the changed environment, and have 
a positive general tendency to adapt the organism to that 
environment, since variation will particularly affect organs 
at once enfeebled and stimulated. This mode of evolution, 
by external forces and the breaking up of habits, seems to 
be called for by some of the broadest and most important 
facts of biology and paleontology; while it certainly has 
been the chief factor in the historical evolution of institu¬ 
tions as in that of ideas; and cannot possibly be refused 
a very prominent place in the process of evolution of the 
universe in general. 

Passing to psychology, we find the elementary phenomena 
of mind fall into three categories. First, we have Feelings, 
comprising all that is immediately present, such as pain, 
blue, cheerfulness, the feeling that arises when we contem- 


166 


LOVE AND CHANCE 


plate a consistent theory, etc. A feeling is a state of mind 
having its own living quality, independent of any other 
state of mind. Or, a feeling is an element of consciousness 
which might conceivably override every other state until it 
monopolized the mind, although such a rudimentary state 
cannot actually be realized, and would not properly be 
consciousness. Still, it is conceivable, or supposable, that 
the quality of blue should usurp the whole mind, to the 
exclusion of the ideas of shape, extension, contrast, com¬ 
mencement and cessation, and all other ideas, whatsoever. 
A feeling is necessarily perfectly simple, in itself , for if it 
had parts these would also be in the mind, whenever the 
whole was present, and thus the whole could not monopolize 
the mind . 3 

Besides Feelings, we have Sensations of reaction; as 
when a person blindfold suddenly runs against a post, when 
we make a muscular effort, or when any feeling gives way 
to a new feeling. Suppose I had nothing in my mind but 
a feeling of blue, which were suddenly to give place to a 
feeling of red; then, at the instant of transition there would 
be a shock, a sense of reaction, my blue life being trans¬ 
muted into red life. If I were further endowed with a 
memory, that sense would continue for some time, and there 
would also be a peculiar feeling or sentiment connected 
with it. This last feeling might endure (conceivably I 
mean) after the memory of the occurrence and the feelings 
of blue and red had passed away. But the sensation of 
reaction cannot exist except in the actual presence of the 

3 A feeling may certainly be compound, but only in virtue of a per¬ 
ception which is not that feeling nor any feeling at all; 


THE ARCHITECTURE OF THEORIES 167 

two feelings blue and red to which it relates. Wherever 
we have two feelings and pay attention to a relation be¬ 
tween them of whatever kind, there is the sensation of 
which I am speaking. But the sense of action and reaction 
has two types: it may either be a perception of relation 
between two ideas, or it may be a sense of action and re¬ 
action between feeling and something out of feeling. And 
this sense of external reaction again has two forms; for it 
is either a sense of something happening to us, by no act of 
ours, we being passive in the matter, or it is a sense of re¬ 
sistance, that is, of our expending feeling upon something 
without. The sense of reaction is thus a sense of connection 
or comparison between feelings, either, A, between one 
feeling and another, or B, between feeling and its absence 
or lower degree; and under B we have, First, the sense of 
the access of feeling, and Second, the sense of remission of 
feeling. 

Very different both from feelings and from reaction- 
sensations or disturbances of feeling are general conceptions. 
When we think, we are conscious that a connection between 
feelings is determined by a general rule, we are aware of 
being governed by a habit. Intellectual power is nothing 
but facility in taking habits and in following them in cases 
essentially analogous to, but in non-essentials widely re¬ 
mote from, the normal cases of connections of feelings under 
which those habits were formed. 

The one primary and fundamental law of mental action 
consists in a tendency to generalization. Feeling tends to 
spread; connections between feelings awaken feelings; 
neighboring feelings become assimilated; ideas are apt to 


168 


LOVE AND CHANCE 


reproduce themselves. These are so many formulations of 
the one law of the growth of mind. When a disturbance 
of feeling takes place, we have a consciousness of gain, the 
gain of experience; and a new disturbance will be apt to 
assimilate itself to the one that preceded it. Feelings, by 
being excited, become more easily excited, especially in the 

ways in which they have previously been excited. The con- 

✓ 

sciousness of such a habit constitutes a general conception. 

The cloudiness of psychological notions may be corrected 
by connecting them with physiological conceptions. Feel- 
ing may be supposed to exist, wherever a nerve-cell is in an 
excited condition. The disturbance of feeling, or sense of 
reaction, accompanies the transmission of disturbance be¬ 
tween nerve-cells or from a nerve-cell to a muscle-cell or 
the external stimulation of a nerve-cell. General concep¬ 
tions arise upon the formation of habits in the nerve-matter, 
which are molecular changes consequent upon its activity 
and probably connected with its nutrition. 

The law of habit exhibits a striking contrast to all physi¬ 
cal laws in the character of its commands. A physical law 
is absolute. What it requires is an exact relation. Thus, 
a physical force introduces into a motion a component 
motion to be combined with the rest by the parallelogram 
of forces; but the component motion must actually take 
place exactly as required by the law of force. On the 
other hand, no exact conformity is required by the mental 
law. Nay, exact conformity would be in downright con¬ 
flict with the law; since it would instantly crystallize thought 
and prevent all further formation of habit. The law of 
mind only makes a given feeling more likely to arise. It 


THE ARCHITECTURE OF THEORIES 


169 


thus resembles the “ non-conservative ” forces of physics, 
such as viscosity and the like, which are due to statistical 
uniformities in the chance encounters of trillions of mole¬ 
cules. 

The old dualistic notion of mind and matter, so prominent 
in Cartesianism, as two radically different kinds of sub¬ 
stance, will hardly find defenders to-day. Rejecting this, 
we are driven to some form of hylopathy, otherwise called 
monism. Then the question arises whether physical laws 
on the one hand, and the psychical law on the other are to 
be taken — 

(A) as independent, a doctrine often called monism , but 
which I would name neutralism; or, 

( B ) the psychical law as derived and special, the physi¬ 
cal law alone as primordial, which is materialism; or, 

(C) the physical law as derived and special, the psychical 
law alone as primordial, which is idealism . 


The materialistic doctrine seems to me quite as repugnant 
to scientific logic as to common sense; since it requires us 
to suppose that a certain kind of mechanism will feel, which 
would be a hypothesis absolutely irreducible to reason,— 
an ultimate, inexplicable regularity; while the only possible 
justification of any theory is that it should make things 
clear and reasonable. 

Neutralism is sufficiently condemned by the logical maxim 
known as Ockham’s razor, i.e., that not more independent 
elements are to be supposed than necessary. By placing 
the inward and outward aspects of substance on a par, it 
seems to render both primordial. 

The one intelligible theory of the universe is that of ob- 


“1 



LOVE AND CHANCE 


170 


jective idealism, that matter is effete mind, inveterate habits 
becoming physical laws. But before this can be accepted 
it must show itself capable of explaining the tridimension¬ 
ality of space, the laws of motion, and the general charac¬ 
teristics of the universe, with mathematical clearness and 
precision; for no less should be demanded of every 
Philosophy. 

Modern mathematics is replete with ideas which may be 
applied to philosophy. I can only notice one or two. The 
manner in which mathematicians generalize is very instruc¬ 
tive. Thus, painters are accustomed to think of a picture 



as consisting geometrically of the intersections of its plane 
by rays of light from the natural objects to the eye. But 
geometers use a generalized perspective. 4 For instance 
in the figure let 0 be the eye, let A B C D E be the edge- 

4 [The reader will find further light on the following illustration in 
any text-book of projective geometry, e.g., Reye, Geometry of Position, 
I, pp. 17-24, or Encye. Britannica, XI, p. 689.] 





THE ARCHITECTURE OF THEORIES 171 

wise view of any plane, and let a f e D c be the edgewise 
view of another plane. The geometers draw rays 
through O cutting both these planes, and treat the points 
of intersection of each ray with one plane as representing 
the point of intersection of the same ray with the other 
plane. Thus, e represents E, in the painter’s way. D 
represents itself. C is represented by c, which is further 
from the eye; and A is represented by a which is on the 
other side of the eye. Such generalization is not bound 
down to sensuous images. Further, according to this mode 
of representation every point on one plane represents a 
point on the other, and every point on the latter is repre¬ 
sented by a point on the former. But how about the point 
/ which is in a direction from O parallel to the represented 
plane, and how about the point B which is in a direction 
parallel to the representing plane? Some will say that 
these are exceptions; but modern mathematics does not 
allow exceptions which can be annulled by generalization. 5 
As a point moves from C to D and thence to E and off 
toward infinity, the corresponding point on the other plane 
moves from c to D and thence to e and toward /. But this 
second point can pass through j to a; and when it is there 
the first point has arrived at A. We therefore say that the 
first point has passed through infinity, and that every line 
joins in to itself somewhat like an oval. Geometers talk of 


5 [A more familiar example of this is the introduction of irrational or 
surd numbers like After it was proved that no ratio of two integers 

could possibly equal V 5 the idea of number was generalized to include the 
latter. Fractions and the so-called imaginary numbers illustrate the same 
process of generalization for the sake of making certain operations (i.e. 
division and finding the root) continuously applicable. 


172 


LOVE AND CHANCE 


the parts of lines at an infinite distance as points. This is 
a kind of generalization very efficient in mathematics. 

Modern views of measurement have a philosophical 
aspect. There is an indefinite number of systems of measur¬ 
ing along a line; thus, a perspective representation of a 
scale on one line may be taken to measure another, although 
of course such measurements will not agree with what we 
call the distances of points on the latter line. To establish 
a system of measurement on a line we must assign a distinct 
number to each point of it, and for this purpose we shall 
plainly have to suppose the numbers carried out into an 
infinite number of places of decimals. These numbers 
must be ranged along the line in unbroken sequence. 
Further, in order that such a scale of numbers should be 
of any use, it must be capable of being shifted into new 
positions, each number continuing to be attached to a single 
distinct point. Now it is found that if this is true for 
“ imaginary ” as well as for real points (an expression 
which I cannot stop to elucidate), any such shifting will 
necessarily leave two numbers attached to the same points 
as before. So that when the scale is moved over the line 
by any continuous series of shiftings of one kind, there are 
two points which no numbers on the scale can ever reach, 
except the numbers fixed there. This pair of points, thus 
unattainable in measurement, is called the Absolute. These 
two points may be distinct and real, or they may coincide, 
or they may be both imaginary. As an example of a linear 
quantity with a double absolute we may take probability, 
which ranges from an unattainable absolute certainty 
against a proposition to an equally unattainable absolute 


THE ARCHITECTURE OF THEORIES 


*73 


certainty for it. A line, according to ordinary notions, we 
have seen is a linear quantity where the two points at infinity 
coincide. A velocity is another example. A train going with 
infinite velocity from Chicago to New York would be at all 
the points on the line at the very same instant, and if the 
time of transit were reduced to less than nothing it would be 
moving in the other direction. An angle is a familiar ex¬ 
ample of a mode of magnitude with no real immeasurable 
values. One of the questions philosophy has to consider 
is whether the development of the universe is like the in¬ 
crease of an angle, so that it proceeds forever without tend¬ 
ing toward anything unattained, which I take to be the 
Epicurean view, or whether the universe sprang from a 
chaos in the infinitely distant past to tend toward some¬ 
thing different in the infinitely distant future, or whether 
the universe sprang from nothing in the past to go on in¬ 
definitely toward a point in the infinitely distant future, 
which, were it attained, would be the mere nothing from 
which it set out. 

The doctrine of the absolute applied to space comes to 
this, that either — 

First, space is, as Euclid teaches, both unlimited and 
immeasurable , so that the infinitely distant parts of any 
plane seen in perspective appear as a straight line, in which 
case the sum of the three angles of a triangle amounts to 
180 0 ; or, 

Second, space is immeasurable but limited , so that the 
infinitely distant parts of any plane seen in perspective 
appear as a circle, beyond which all is blackness, and in 
this case the sum of the three angles of a triangle is less 


174 


LOVE AND CHANCE 


than i8o° by an amount proportional to the area of the 
triangle; or, 

Third, space is unlimited but finite , (like the surface of 
a sphere), so that it has no infinitely distant parts; but a 
finite journey along any straight line would bring one back 
to his original position, and looking off with an unobstructed 
view one would see the back of his own head enormously 
magnified, in which case the sum of the three angles of a 
triangle exceeds i8o° by an amount proportional to the 
area. 

Which of these three hypotheses is true we know not. 
The largest triangles we can measure are such as have the 
earth’s orbit for base, and the distance of a fixed star for 
altitude. The angular magnitude resulting from subtract¬ 
ing the sum of the two angles at the base of such a triangle 
from i8o° is called the star’s parallax . The parallaxes of 
only about forty stars have been measured as yet. Two 
of them come out negative, that of Arided (a Cycni), a 
star of magnitude ij, which is — o."o82, according to C. A. 
F. Peters, and that of a star of magnitude 7f, known as 
Piazzi III 422, which is — o."o45, according to R. S. Ball. 
But these negative parallaxes are undoubtedly to be at¬ 
tributed to errors of observation; for the probable error of 
such a determination is about ± o."o75, and it would be 
strange indeed if we were to be able to see, as it were, 
more than half way round space, without being able to see 
stars with larger negative parallaxes. Indeed, the very 
fact that of all the parallaxes measured only two come out 
negative would be a strong argument that the smallest 
parallaxes really amount to + o/T, were it not for the re- 


THE ARCHITECTURE OF THEORIES 


17 s 

flection that the publication of other negative parallaxes 
may have been suppressed. I think we may feel confident 
that the parallax of the furthest star lies somewhere between 
— o."o5 and + o/'i5,and within another century our grand¬ 
children will surely know whether the three angles of a 
triangle are greater or less than 180°, — that they are 
exactly that amount is what nobody ever can be justified in 
concluding. It is true that according to the axioms of 
geometry the sum of the three sides of a triangle are pre¬ 
cisely 180 0 ; but these axioms are now exploded, and 
geometers confess that they, as geometers, know not the 
slightest reason for supposing them to be precisely true. 
They are expressions of our inborn conception of space, 
and as such are entitled to credit, so far as their truth could 
have influenced the formation of the mind. But that af¬ 
fords not the slightest reason for supposing them exact. 

Now, metaphysics has always been the ape of mathe¬ 
matics. Geometry suggested the idea of a demonstrative 
system of absolutely certain philosophical principles; and 
the ideas of the metaphysicians have at all times been in 
large part drawn from mathematics. The metaphysical 
axioms are imitations of the geometrical axioms; and now 
that the latter have been thrown overboard, without doubt 
the former will be sent after them. It is evident, for in¬ 
stance, that we can have no reason to think that every 
phenomenon in all its minutest details is precisely deter¬ 
mined by law. That there is an arbitrary element in the 
universe we see, — namely, its variety. This variety must 
be attributed to spontaneity in some form. 

Had I more space, I now ought to show how important 


176 


LOVE AND CHANCE 


for philosophy is the mathematical conception of continuity. 
Most of what is true in Hegel is a darkling glimmer of a 
conception which the mathematicians had long before made 
pretty clear, and which recent researches have still further 
illustrated. 

Among the many principles of Logic which find their 
application in Philosophy, I can here only mention one. 
Three conceptions are perpetually turning up at every point 
in every theory of logic, and in the most rounded systems 
they occur in connection with one another. They are con¬ 
ceptions so very broad and consequently indefinite that they 
are hard to seize and may be easily overlooked. I call 
them the conceptions of First, Second, Third. First is the 
conception of being or existing independent of anything else. 
Second is the conception of being relative to, the concep¬ 
tion of reaction with, something else. Third is the con¬ 
ception of mediation, whereby a first and second are brought 
into relation. To illustrate these ideas, I will show how 
they enter into those we have been considering. The origin 
of things, considered not as leading to anything, but in 
itself, contains the idea of First, the end of things that of 
Second, the process mediating between them that of Third. 
A philosophy which emphasizes the idea of the One, is 
generally a dualistic philosophy in which the conception 
of Second receives exaggerated attention; for this One 
(though of course involving the idea of First) is always 
the other of a manifold which is not one. The idea of the 
Many, because variety is arbitrariness and arbitrariness is 
repudiation of any Secondness, has for its principal com¬ 
ponent the conception of First. In psychology Feeling is 


THE ARCHITECTURE OF THEORIES 


177 


First, Sense of reaction Second, General conception Third, 
or mediation. In biology, the idea of arbitrary sporting is 
First, heredity is Second, the process whereby the accidental 
characters become fixed is Third. Chance is First, Law 
is Second, the tendency to take habits is Third. Mind is 
First, Matter is Second, Evolution is Third. 

Such are the materials out of which chiefly a philosophical 
theory ought to be built, in order to represent the state of 
knowledge to which the nineteenth century has brought us. 
Without going into other important questions of philoso¬ 
phical architectonic, we can readily foresee what sort of 
a metaphysics would appropriately be constructed from 
those conceptions. Like some of the most ancient and 
some of the most recent speculations it would be a Cosmo¬ 
gonic Philosophy. It would suppose that in the beginning, 
— infinitely remote, — there was a chaos of unpersonalized 
feeling, which being without connection or regularity would 
properly be without existence. This feeling, sporting here 
and there in pure arbitrariness, would have started the germ 
of a generalizing tendency. Its other sportings would be 
evanescent, but this would have a growing virtue. Thus, 
the tendency to habit would be started; and from this with 
the other principles of evolution all the regularities of the 
universe would be evolved. At any time, however, an 
element of pure chance survives and will remain until the 
world becomes an absolutely perfect, rational, and sym¬ 
metrical system, in which mind is at last crystallized in the 
infinitely distant future. 

That idea has been worked out by me with elaboration. 
It accounts for the main features of the universe as we 


178 


LOVE AND CHANCE 


know it, — the characters of time, space, matter, force, 
gravitation, electricity, etc. It predicts many more things 
which new observations can alone bring to the test. May 
some future student go over this ground again, and have the 
leisure to give his results to the world. 


II. THE DOCTRINE OF NECESSITY EXAMINED 1 


In The Monist for January, 1891, I endeavored to show 
what elementary ideas ought to enter into our view of the 
universe. I may mention that on those considerations I 
had already grounded a cosmical theory, and from it had 
deduced a considerable number of consequences capable 
of being compared with experience. This comparison is 
now in progress, but under existing circumstances must 
occupy many years. 

I propose here to examine the common belief that every 
single fact in the universe is precisely determined by law. 
It must not be supposed that this is a doctrine accepted 
everywhere and at all times by all rational men. Its first 
advocate appears to have been Democritus, the atomist, who 
was led to it, as we are informed, by reflecting upon the 
“ impenetrability, translation, and impact of matter 

(avTiTViria Kal 4>opa kclI TrXrjyrj rrjs v\i 7s).” That is to 
say, having restricted his attention to a field where no influ¬ 
ence other than mechanical constraint could possibly come 
before his notice, he straightway jumped to the conclusion 
that throughout the universe that was the sole principle of 
action, — a style of reasoning so usual in our day with men 
not unreflecting as to be more than excusable in the in¬ 
fancy of thought. But Epicurus, in revising the atomic 
doctrine and repairing its defences, found himself obliged 

1 The Monist, April, 1892. 

179 


LOVE AND CHANCE 


180 

to suppose that atoms swerve from their courses by spon¬ 
taneous chance; and thereby he conferred upon the theory 
life and entelechy. For we now see clearly that the pe¬ 
culiar function of the molecular hypothesis in physics is 
to open an entry for the calculus of probabilities. Already, 
the prince of philosophers had repeatedly and emphatically 
condemned the dictum of Democritus (especially in the 
“ Physics,” Book II, chapters iv, v, vi), holding that events 
come to pass in three ways, namely, (i) by external com¬ 
pulsion, or the action of efficient causes, (2) by virtue of 
an inward nature, or the influence of final causes, and (3) 
irregularly without definite cause, but just by absolute 
chance; and this doctrine is of the inmost essence of Aris- 
totelianism. It affords, at any rate, a valuable enumeration 
of the possible ways in which anything can be supposed 
to have come about. The freedom of the will, too, was 
admitted both by Aristotle and by Epicurus. But the Stoa, 
which in every department seized upon the most tangible, 
hard, and lifeless element, and blindly denied the existence 
of every other, which, for example, impugned the validity 
of the inductive method and wished to fill its place with the 
reductio ad absurdum, very naturally became the one school 
of ancient philosophy to stand by a strict necessitarianism, 
thus returning to a single principle of Democritus that 
Epicurus had been unable to swallow. Necessitarianism 
and materialism with the Stoics went hand in hand, as by 
affinity they should. At the revival of learning, Stoicism 
met with considerable favor, partly because it departed 
just enough from Aristotle to give it the spice of novelty, 
and partly because its superficialities well adapted it for 


DOCTRINE OF NECESSITY EXAMINED 181 

acceptance by students of literature and art who wanted 
their philosophy drawn mild. Afterwards, the great dis¬ 
coveries in mechanics inspired the hope that mechanical 
principles might suffice to explain the universe; and though 
without logical justification, this hope has since been con¬ 
tinually stimulated by subsequent advances in physics. 
Nevertheless, the doctrine was in too evident conflict with 
the freedom of the will and with miracles to be generally 
acceptable, at first. But meantime there arose that most 
widely spread of philosophical blunders, the notion that 
associationalism belongs intrinsically to the materialistic 
family of doctrines; and thus was evolved the theory of 
motives; and libertarianism became weakened. At present, 
historical criticism has almost exploded the miracles, great 
and small; so that the doctrine of necessity has never been 
in so great vogue as now. 

The proposition in question is that the state of things 
existing at any time, together with certain immutable laws, 
completely determine the state of things at every other time 
(for a limitation to future time is indefensible). Thus, 
given the state of the universe in the original nebula, and 
given the laws of mechanics, a sufficiently powerful mind 
could deduce from these data the precise form of every 
curlicue of every letter I am now writing. 

Whoever holds that every act of the will as well as every 
idea of the mind is under the rigid governance of a neces¬ 
sity co-ordinated with that of the physical world, will logi¬ 
cally be carried to the proposition that minds are part of 
the physical world in such a sense that the laws of me¬ 
chanics determine everything that happens according to 


i8z 


LOVE AND CHANCE 


immutable attractions and repulsions. In that case, that 
instantaneous state of things from which every other state 
of things is calculable consists in the positions and velocities 
of all the particles at any instant. This, the usual and 
most logical form of necessitarianism, is called the mechani¬ 
cal philosophy. 

When I have asked thinking men what reason they had 
to believe that every fact in the universe is precisely de¬ 
termined by law, the first answer has usually been that 
the proposition is a “ presupposition ” or postulate of scien¬ 
tific reasoning. Well, if that is the best that can be said 
for it, the belief is doomed. Suppose it be “ postulated 
that does not make it true, nor so much as afford the slight¬ 
est rational motive for yielding it any credence. It is as 
if a man should come to borrow money, and when asked 
for his security, should reply he “ postulated ” the loan. 
To “ postulate ” a proposition is no more than to hope it is 
true. There are, indeed, practical emergencies in which 
we act upon assumptions of certain propositions as true, 
because if they are not so, it can make no difference how 
we act. But all such propositions I take to be hypotheses 
of individual facts. For it is manifest that no universal 
principle can in its universality be comprised in a special 
case or can be requisite for the validity of any ordinary 
inference. To say, for instance, that the demonstration 
by Archimedes of the property of the lever would fall to 
the ground if men were endowed with free-will, is extrava¬ 
gant; yet this is implied by those who make a proposition 
incompatible with the freedom of the will the postulate of 
all inference. Considering, too, that the conclusions of 


DOCTRINE OF NECESSITY EXAMINED 183 

science make no pretence to being more than probable, and 
considering that a probable inference can at most only 
suppose something to be most frequently, or otherwise 
approximately, true, but never that anything is precisely 
true without exception throughout the universe, we see how 
far this proposition in truth is from being so postulated. 

But the whole notion of a postulate being involved in 
reasoning appertains to a by-gone and false conception of 
logic. Non-deductive, or ampliative inference, is of three 
kinds: induction, hypothesis, and analogy. If there be 
any other modes, they must be extremely unusual and 
highly complicated, and may be assumed with little doubt 
to be of the same nature as those enumerated. For induc¬ 
tion, hypothesis, and analogy, as far as their ampliative 
character goes, that is, so far as they conclude something 
not implied in the premises, depend upon one principle and 
involve the same procedure. All are essentially inferences 
from sampling. Suppose a ship arrives at Liverpool laden 
with wheat in bulk. Suppose that by some machinery the 
whole cargo be stirred up with great thoroughness. Sup¬ 
pose that twenty-seven thimblefuls be taken equally from 
the forward, midships, and aft parts, from the starboard, 
center, and larboard parts, and from the top, half depth, 
and lower parts of her hold, and that these being mixed 
and the grains counted, four-fifths of the latter are found 
to be of quality A. Then we infer, experientially and pro¬ 
visionally, that approximately four-fifths of all the grain in 
the cargo is of the same quality. I say we infer this ex¬ 
perientially and provisionally . By saying that we infer it 
experientially , I mean that our conclusion makes no pre- 


184 


LOVE AND CHANCE 


tension to knowledge of wheat-in-itself, our aXTjdeLa, 
as the derivation of that word implies, has nothing to do 
with latent wheat. We are dealing only with the matter 
of possible experience, — experience in the full acceptation 
of the term as something not merely affecting the senses 
but also as the subject of thought. If there be any wheat 
hidden on the ship, so that it can neither turn up in the 
sample nor be heard of subsequently from purchasers, — 
or if it be half-hidden, so that it may, indeed, turn up, but 
is less likely to do so than the rest, — or if it can affect our 
senses and our pockets, but from some strange cause or 
causelessness cannot be reasoned about, — all such wheat 
is to be excluded (or have only its proportional weight) in 
calculating that true proportion of quality A, to which our 
inference seeks to approximate. By saying that we draw 
the inference provisionally, I mean that we do not hold 
that we have reached any assigned degree of approximation 
as yet, but only hold that if our experience be indefinitely 
extended, and if every fact of whatever nature, as fast as it 
presents itself, be duly applied, according to the inductive 
method, in correcting the inferred ratio, then our approxi¬ 
mation will become indefinitely close in the long run; that 
is to say, close to the experience to come (not merely close 
by the exhaustion of a finite collection) so that if experience 
in general is to fluctuate irregularly to and fro, in a manner 
to deprive the ratio sought of all definite value, we shall 
be able to find out approximately within what limits it 
fluctuates, and if, after having one definite value, it changes 
and assumes another, we shall be able to find that out, and 
in short, whatever may be the variations of this ratio in 


DOCTRINE OF NECESSITY EXAMINED 


185 


experience, experience indefinitely extended will enable us 
to detect them, so as to predict rightly, at last, what its 
ultimate value may be, if it have any ultimate value, or 
what the ultimate law of succession of values may be, if 
there be any such ultimate law, or that it ultimately fluc¬ 
tuates irregularly within certain limits, if it do so ultimately 
fluctuate. Now our inference, claiming to be no more than 
thus experiential and provisional, manifestly involves no 
postulate whatever. 

For what is a postulate? It is the formulation of a ma¬ 
terial fact which we are not entitled to assume as a premise, 
but the truth of which is requisite to the validity of an 
inference. Any fact, then, which might be supposed postu¬ 
lated, must either be such that it would ultimately present 
itself in experience, or not. If it will present itself, we 
need not postulate it now in our provisional inference, since 
we shall ultimately be entitled to use it as a premise. But 
if it never would present itself in experience, our conclusion 
is valid but for the possibility of this fact being otherwise 
than assumed, that is, it is valid as far as possible experi¬ 
ence goes, and that is all that we claim. Thus, every 
postulate is cut off, either by the provisionality or by the 
experientiality of our inference. For instance, it has been 
said that induction postulates that, if an indefinite succes¬ 
sion of samples be drawn, examined, and thrown back each 
before the next is drawn, then in the long run every grain 
will be drawn as often as any other, that is to say, postulates 
that the ratio of the numbers of times in which any two 
are drawn will indefinitely approximate to unity. But no 
such postulate is made; for if, on the one hand, we are to 


186 


LOVE AND CHANCE 


have no other experience of the wheat than from such 
drawings, it is the ratio that presents itself in those drawings 
and not the ratio which belongs to the wheat in its latent 
existence that we are endeavoring to determine; while if, 
on the other hand, there is some other mode by which the 
wheat is to come under our knowledge, equivalent to an¬ 
other kind of sampling, so that after all our care in stirring 
up the wheat, some experiential grains will present them¬ 
selves in the first sampling operation more often than others 
in the long run, this very singular fact will be sure to get 
discovered by the inductive method, which must avail itself 
of every sort of experience; and our inference, which was 
only provisional, corrects itself at last. Again, it has been 
said, that induction postulates that under like circumstances 
like events will happen, and that this postulate is at bottom 
the same as the principle of universal causation. But this 
is a blunder, or bevue, due to thinking exclusively of in¬ 
ductions where the concluded ratio is either i or o. If 
any such proposition were postulated, it would be that 
under like circumstances (the circumstances of drawing the 
different samples) different events occur in the same pro- 
portions in all the different sets, — a proposition which is 
false and even absurd. But in truth no such thing is postu¬ 
lated, the experiential character of the inference reducing 
the condition of validity to this, that if a certain result does 
not occur, the opposite result will be manifested, a condition 
assured by the provisionality of the inference. But it may 
be asked whether it is not conceivable that every instance 
of a certain class destined to be ever employed as a datum 
of induction should have one character, while every instance 


DOCTRINE OF NECESSITY EXAMINED 


187 


destined not to be so employed should have the opposite 
character. The answer is that in that case, the instances 
excluded from being subjects of reasoning would not be 
experienced in the full sense of the word, but would be 
among these latent individuals of which our conclusion does 
not pretend to speak. 

To this account of the rationale of induction I know of 
but one objection worth mention: it is that I thus fail to 
deduce the full degree of force which this mode of inference 
in fact possesses; that according to my view, no matter 
how thorough and elaborate the stirring and mixing process 
had been, the examination of a single handful of grain 
would not give me any assurance, sufficient to risk money 
upon that the next handful would not greatly modify the 
concluded value of the ratio under inquiry, while, in fact, 
the assurance would be very high that this ratio was not 
greatly in error. If the true ratio of grains of quality A 
were 0.80 and the handful contained a thousand grains, 
nine such handfuls out of every ten would contain from 
780 to 820 grains of quality A. The answer to this is that 
the calculation given is correct when we know that the units 
of this handful and the quality inquired into have the nor¬ 
mal independence of one another, if for instance the stirring 
has been complete and the character sampled for has been 
settled upon in advance of the examination of the sample. 
But in so far as these conditions are not known to be com¬ 
plied with, the above figures cease to be applicable. Ran¬ 
dom sampling and predesignation of the character sampled 
for should always be striven after in inductive reasoning, 
but when they cannot be attained, so long as it is conducted 


188 


LOVE AND CHANCE 


honestly, the inference retains some value. When we can¬ 
not ascertain how the sampling has been done or the sample- 
character selected, induction still has the essential validity 
which my present account of it shows it to have. 

I do not think a man who combines a willingness to be 
convinced with a power of appreciating an argument upon 
a difficult subject can resist the reasons which have been 
given to show that the principle of universal necessity can¬ 
not be defended as being a postulate of reasoning. But then 
the question immediately arises whether it is not proved to 
be true, or at least rendered highly probable, by observa¬ 
tion of nature. 

Still, this question ought not long to arrest a person 
accustomed to reflect upon the force of scientific reasoning. 
For the essence of the necessitarian position is that certain 
continuous quantities have certain exact values. Now, how 
can observation determine the value of such a quantity with 
a probable error absolutely nil? To one who is behind the 
scenes, and knows that the most refined comparisons of 
masses, lengths, and angles, far surpassing in precision all 
other measurements, yet fall behind the accuracy of bank- 
accounts, and that the ordinary determinations of physi¬ 
cal constants, such as appear from month to month in the 
journals, are about on a par with an upholsterer’s measure¬ 
ments of carpets and curtains, the idea of mathematical 
exactitude being demonstrated in the laboratory will appear 
simply ridiculous. There is a recognized method of esti¬ 
mating the probable magnitudes of errors in physics, — the 
method of least squares. It is universally admitted that 
this method makes the errors smaller than they really are; 


DOCTRINE OF NECESSITY EXAMINED 


189 


yet even according to that theory an error indefinitely small 
is indefinitely improbable; so that any statement to the 
effect that a certain continuous quantity has a certain exact 
value, if well-founded at all, must be founded on something 
other than observation. 

Still, I am obliged to admit that this rule is subject to a 
certain qualification. Namely, it only applies to continuous 2 
quantity. Now, certain kinds of continuous quantity are 
discontinuous at one or at two limits, and for such limits 
the rule must be modified. Thus, the length of a line can¬ 
not be less than zero. Suppose, then, the question arises 
how long a line a certain person had drawn from a marked 
point on a piece of paper. If no line at all can be seen, the 
observed length is zero; and the only conclusion this obser¬ 
vation warrants is that the length of the line is less than the 
smallest length visible with the optical power employed. 
But indirect observations, — for example, that the person 
supposed to have drawn the line was never within fifty 
feet of the paper, — may make it probable that no line 
at all was made, so that the concluded length will be strictly 
zero. In like manner, experience no doubt would warrant 
the conclusion that there is absolutely no indigo in a given 
ear of wheat, and absolutely no attar in a given lichen. 
But such inferences can only be rendered valid by posi¬ 
tive experiential evidence, direct or remote, and cannot rest 
upon a mere inability to detect the quantity in question. 
We have reason to think there is no indigo in the wheat, 
because we have remarked that wherever indigo is pro- 

2 Continuous is not exactly the right word, but I let it go to avoid a 
long and irrelevant discussion. 


190 


LOVE AND CHANCE 


duced it is produced in considerable quantities, to mention 
only one argument. We have reason to think there is no 
attar in the lichen, because essential oils seem to be in 
general peculiar to single species. If the question had been 
whether there was iron in the wheat or the lichen, though 
chemical analysis should fail to detect its presence, we 
should think some of it probably was there, since iron is 
almost everywhere. Without any such information, one 
way or the other, we could only abstain from any opinion as 
to the presence of the substance in question. It cannot, I 
conceive, be maintained that we are in any better position 
than this in regard to the presence of the element of chance 
or spontaneous departures from law in nature. 

Those observations which are generally adduced in favor 
of mechanical causation simply prove that there is an ele¬ 
ment of regularity in nature, and have no bearing what¬ 
ever upon the question of whether such regularity is exact 
and universal, or not. Nay, in regard to this exactitude , all 
observation is directly opposed to it; and the most that can 
be said is that a good deal of this observation can be ex¬ 
plained away. Try to verify any law of nature, and you 
will find that the more precise your observations, the more 
certain they will be to show irregular departures from the 
law. We are accustomed to ascribe these, and I do not 
say wrongly, to errors of observation; yet we cannot usually 
account for such errors in any antecedently probable way. 
Trace their causes back far enough, and you will be forced 
to admit they are always due to arbitrary determination, 
or chance. 

But it may be asked whether if there were an element 


DOCTRINE OF NECESSITY EXAMINED 191 

of real chance in the universe it must not occasionally be 
productive of signal effects such as could not pass un¬ 
observed. In answer to this question, without stopping to 
point out that there is an abundance of great events which 
one might be tempted to suppose were of that nature, it will 
be simplest to remark that physicists hold that the particles 
of gases are moving about irregularly, substantially as if 
by real chance, and that by the principles of probabilities 
there must occasionally happen to be concentrations of heat 
in the gases contrary to the second law of thermodynamics, 
and these concentrations, occurring in explosive mixtures, 
must sometimes have tremendous effects. Here, then, is 
in substance the very situation supposed; yet no phenomena 
ever have resulted which we are forced to attribute to such 
chance concentration of heat, or which anybody, wise or 
foolish, has ever dreamed of accounting for in that manner. 

In view of all these considerations, I do not believe that 
anybody, not in a state of case-hardened ignorance respect¬ 
ing the logic of science, can maintain that the precise and 
universal conformity of facts to law is clearly proved, or 
even rendered particularly probable, by any observations 
hitherto made. In this way, the determined advocate of 
exact regularity will soon find himself driven to a priori 
reasons to support his thesis. These received such a soc- 
dolager from Stuart Mill in his Examination of Hamilton, 
that holding to them now seems to me to denote a high 
degree of imperviousness to reason; so that I shall pass 
them by with little notice. 

To say that we cannot help believing a given proposi¬ 
tion is no argument, but it is a conclusive fact if it be 


192 


LOVE AND CHANCE 


true; and with the substitution of “I” for “we,” it is 
true in the mouths of several classes of minds, the blindly 
passionate, the unreflecting and ignorant, and the per¬ 
son who has overwhelming evidence before his eyes. But 
that which has been inconceivable to-day has often turned 
out indisputable on the morrow. Inability to conceive is 
only a stage through which every man must pass in regard 
to a number of beliefs, — unless endowed with extraordinary 
obstinacy and obtuseness. His understanding is enslaved 
to some blind compulsion which a vigorous mind is pretty 
sure soon to cast off. 

Some seek to back up the a priori position with empirical 
arguments. They say that the exact regularity of the world 
is a natural belief, and that natural beliefs have generally 
been confirmed by experience. There is some reason in 
this. Natural beliefs, however, if they generally have a 
foundation of truth, also require correction and purification 
from natural illusions. The principles of mechanics are un¬ 
doubtedly natural beliefs; but, for all that, the early formu¬ 
lations of them were exceedingly erroneous. The general 
approximation to truth in natural beliefs is, in fact, a case 
of the general adaptation of genetic products to recogniz¬ 
able utilities or ends. Now, the adaptations of nature, 
beautiful and often marvelous as they verily are, are never 
found to be quite perfect; so that the argument is quite 
against the absolute exactitude of any natural belief, in¬ 
cluding that of the principle of causation. 

Another argument, or convenient commonplace, is that 
absolute chance is inconceivable. (This word has eight cur¬ 
rent significations. The Century Dictionary enumerates 


DOCTRINE OF NECESSITY EXAMINED 


193 


six.) Those who talk like this will hardly be persuaded 
to say in what sense they mean that chance is inconceiv¬ 
able. Should they do so, it would easily be shown either 
that they have no sufficient reason for the statement or 
that the inconceivability is of a kind which does not prove 
that chance is non-existent. 

Another a priori argument is that chance is unintelligible; 
that is to say, while it may perhaps be conceivable, it does 
not disclose to the eye of reason the how or why of things; 
and since a hypothesis can only be justified so far as it 
renders some phenomenon intelligible, we never can have 
any right to suppose absolute chance to enter into the 
production of anything in nature. This argument may be 
considered in connection with two others. Namely, instead 
of going so far as to say that the supposition of chance can 
never properly be used to explain any observed fact, it 
may be alleged merely that no facts are known which such 
a supposition could in any way help in explaining. Or 
again, the allegation being still further weakened, it may be 
said that since departures from law are not unmistakably 
observed, chance is not a vera causa, and ought not un¬ 
necessarily to be introduced into a hypothesis. 

These are no mean arguments, and require us to examine 
the matter a little more closely. Come, my superior op¬ 
ponent, let me learn from your wisdom. It seems to me 
that every throw of sixes with a pair of dice is a manifest 
instance of chance. 

“ While you would hold a throw of deuce-ace to be 
brought about by necessity? ” (The opponent’s supposed 
remarks are placed in quotation marks.) 


194 


LOVE AND CHANCE 


Clearly one throw is as much chance as another. 

“ Do you think throws of dice are of a different nature 
from other events? ” 

I see that I must say that all the diversity and specifical- 
ness of events is attributable to chance. 

“ Would you, then, deny that there is any regularity in 
the world? ” 

That is clearly undeniable. I must acknowledge there 
is an approximate regularity, and that every event is in¬ 
fluenced by it. But the diversification, specificalness, and 
irregularity of things I suppose is chance. A throw of 
sixes appears to me a case in which this element is par¬ 
ticularly obtrusive. 

“ If you reflect more deeply, you will come to see that 
chance is only a name for a cause that is unknown to us.” 

Do you mean that we have no idea whatever what kind 
of causes could bring about a throw of sixes? 

“ On the contrary, each die moves under the influence 
of precise mechanical laws.” 

But it appears to me that it is not these laws which made 
the die turn up sixes; for these laws act just the same when 
other throws come up. The chance lies in the diversity of 
throws; and this diversity cannot be due to laws which are 
immutable. 

“ The diversity is due to the diverse circumstances under 
which the laws act. The dice lie differently in the box, 
and the motion given to the box is different. These are the 
unknown causes which produce the throws, and to which 
we give the name of chance; not the mechanical law which 
regulates the operation of these causes. You see you are 
already beginning to think more clearly about this subject.” 



DOCTRINE OF NECESSITY EXAMINED 


195 


Does the operation of mechanical law not increase the 
diversity? 

“ Properly not. You must know that the instantaneous 
state of a system of particles is defined by six times as many 
numbers as there are particles, three for the co-ordinates 

A 

of each particle’s position, and three more for the com¬ 
ponents of its velocity. This number of numbers, which 
expresses the amount of diversity in the system, remains 
the same at all times. There may be, to be sure, some 
kind of relation between the co-ordinates and component 
velocities of the different particles, by means of which the 
state of the system might be expressed by a smaller number 
of numbers. But, if this is the case, a precisely correspond¬ 
ing relationship must exist between the co-ordinates and 
component velocities at any other time, though it may 
doubtless be a relation less obvious to us. Thus, the in¬ 
trinsic complexity of the system is the same at all times.” 

Very well, my obliging opponent, we have now reached an 
issue. You think all the arbitrary specifications of the 
universe were introduced in one dose, in the beginning, if 
there was a beginning, and that the variety and complica¬ 
tion of nature has always been just as much as it is now. 
But I, for my part, think that the diversification, the speci¬ 
fication, has been continually taking place. Should you 
condescend to ask me why I so think, I should give my 
reasons as follows: 

(1) Question any science which deals with the course of 
time. Consider the life of an individual animal or plant, 
or of a mind. Glance at the history of states, of insti¬ 
tutions, of language, of ideas. Examine the successions of 


196 


LOVE AND CHANCE 


forms shown by paleontology, the history of the globe as 
set forth in geology, of what the astronomer is able to 
make out concerning the changes of stellar systems. 
Everywhere the main fact is growth and increasing com¬ 
plexity. Death and corruption are mere accidents or secon¬ 
dary phenomena. Among some of the lower organisms, it 
is a moot point with biologists whether there be anything 
which ought to be called death. Races, at any rate, do not 
die out except under unfavorable circumstances. From 
these broad and ubiquitous facts we may fairly infer, by 
the most unexceptionable logic, that there is probably in 
nature some agency by which the complexity and diversity 
of things can be increased; and that consequently the 
rule of mechanical necessity meets in some way with 
interference. 

(2) By thus admitting pure spontaneity or life as a char¬ 
acter of the universe, acting always and everywhere though 
restrained within narrow bounds by law, producing in¬ 
finitesimal departures from law continually, and great ones 
with infinite infrequency, I account for all the variety and 
diversity of the universe, in the only sense in which the 
really sui generis and new can be said to be accounted for. 
The ordinary view has to admit the inexhaustible multi¬ 
tudinous variety of the world, has to admit that its me¬ 
chanical law cannot account for this in the least, that 
variety can spring only from spontaneity, and yet denies 
without any evidence or reason the existence of this spon¬ 
taneity, or else shoves it back to the beginning of time and 
supposes it dead ever since. The superior logic of my view 
appears to me not easily controverted. 


DOCTRINE OF NECESSITY EXAMINED 


J 97 


(3) When I ask the necessitarian how he would explain 
the diversity and irregularity of the universe, he replies to 
me out of the treasury of his wisdom that irregularity is 
something which from the nature of things we must not 
seek to explain. Abashed at this, I seek to cover my con¬ 
fusion by asking how he would explain the uniformity and 
regularity of the universe, whereupon he tells me that the 
laws of nature are immutable and ultimate facts, and no 
account is to be given of them. But my hypothesis of 
spontaneity does explain irregularity, in a certain sense; 
that is, it explains the general fact of irregularity, though 
not, of course, what each lawless event is to be. At the 
same time, by thus loosening the bond of necessity, it gives 
room for the influence of another kind of causation, such 
as seems to be operative in the mind in the formation of 
associations, and enables us to understand how the uni¬ 
formity of nature could have been brought about. That 
single events should be hard and unintelligible, logic will 
permit without difficulty: we do not expect to make the 
shock of a personally experienced earthquake appear natural 
and reasonable by any amount of cogitation. But logic 
does expect things general to be understandable. To say 
that there is a universal law, and that it is a hard, ultimate, 
unintelligible fact, the why and wherefore of which can 
never be inquired into, at this a sound logic will revolt; 
and will pass over at once to a method of philosophizing 
which does not thus barricade the road of discovery. 

(4) Necessitarianism cannot logically stop short of mak¬ 
ing the whole action of the mind a part of the physical 
universe. Our notion that we decide what we are going to 


LOVE AND CHANCE 


198 

do, if as the necessitarian says, it has been calculable since 
the earliest times, is reduced to illusion. Indeed, conscious¬ 
ness in general thus becomes a mere illusory aspect of a 
material system. What we call red, green, and violet are 
in reality only different rates of vibration. The sole reality 
is the distribution of qualities of matter in space and time. 
Brain-matter is protoplasm in a certain degree and kind of 
complication, — a certain arrangement of mechanical par¬ 
ticles. Its feeling is but an inward aspect, a phantom. 
For, from the positions and velocities of the particles at any 
one instant, and the knowledge of the immutable forces, 
the positions at all other tknes are calculable; so that the 
universe of space, time, and matter is a rounded system 
uninterfered with from elsewhere. But from the state of 
feeling at any instant, there is no reason to suppose the 
states of feeling at all other instants are thus exactly cal¬ 
culable; so that feeling is, as I said, a mere fragmentary 
and illusive aspect of the universe. This is the way, then, 
that necessitarianism has to make up its accounts. It enters 
consciousness under the head of sundries, as a forgotten 
trifle; its scheme of the universe would be more satisfactory 
if this little fact could be dropped out of sight. On the 
other hand, by supposing the rigid exactitude of causation 
to yield, I care not how little, — be it but by a strictly 
infinitesimal amount, — we gain room to insert mind into 
our scheme, and to put it into the place where it is needed, 
into the position which, as the sole self-intelligible thing, 
it is entitled to occupy, that of the fountain of existence; 
and in so doing we resolve the problem of the connection of 
soul and body. 


DOCTRINE OF NECESSITY EXAMINED 


199 


(5) But I must leave undeveloped the chief of my reasons, 
and can only adumbrate it. The hypothesis of chance- 
spontaneity is one whose inevitable consequences are capable 
of being traced out with mathematical precision into con¬ 
siderable detail. Much of this I have done and find the 
consequences to agree with observed facts to an extent 
which seems to me remarkable. But the matter and 
methods of reasoning are novel, and I have no right to 
promise that other mathematicians shall find my deductions 
as satisfactory as I myself do, so that the strongest reason 
for my belief must for the present remain a private reason 
of my own, and cannot influence others. I mention it to 
explain my own position; and partly to indicate to future 
mathematical speculators a veritable goldmine, should time 
and circumstances and the abridger of all joys prevent my 
opening it to the world. 

If now I, in my turn, inquire of the necessitarian why 
he prefers to suppose that all specification goes back to the 
beginning of things, he will answer me with one of those 
last three arguments which I left unanswered. 

First, he may say that chance is a thing absolutely un¬ 
intelligible, and, therefore, that we never can be entitled 
to make such a supposition. But does not this objection 
smack of naive impudence? It is not mine, it is his own 
conception of the universe which leads abruptly up to hard, 
ultimate, inexplicable, immutable law, on the one hand, and 
to inexplicable specification and diversification of circum¬ 
stances on the other. My view, on the contrary, hypothe- 
tises nothing at all, unless it be hypothesis to say that all 
specification came about in some sense, and is not to be 


200 


LOVE AND CHANCE 


accepted as unaccountable. To undertake to account for 
anything by saying boldly that it is due to chance would, 
indeed, be futile. But this I do not do. I make use of 
chance chiefly to make room for a principle of generaliza¬ 
tion, or tendency to form habits, which I hold has produced 
all regularities. The mechanical philosopher leaves the 
whole specification of the world utterly unaccounted for, 
which is pretty nearly as bad as to boldly attribute it to 
chance. I attribute it altogether to chance, it is true, but 
to chance in the form of a spontaneity which is to some 
degree regular. It seems to me clear at any rate that one 
of these two positions must be taken, or else specification 
must be supposed due to a spontaneity which develops itself 
in a certain and not in a chance way, by an objective logic 
like that of Hegel. This last way I leave as an open possi¬ 
bility, for the present; for it is as much opposed to the 
necessitarian scheme of existence as my own theory is. 

Secondly, the necessitarian may say there are, at any rate, 
no observed phenomena which the hypothesis of chance 
could aid in explaining. In reply, I point first to the phe¬ 
nomenon of growth and developing complexity, which ap¬ 
pears to be universal, and which though it may possibly be 
an affair of mechanism perhaps, certainly presents all the 
appearance of increasing diversification. Then, there is 
variety itself, beyond comparison the most obtrusive char¬ 
acter of the universe: no mechanism can account for this. 
Then, there is the very fact the necessitarian most insists 
upon, the regularity of the universe which for him serves 
only to block the road of inquiry. Then, there are the 
regular relationships between the laws of nature, — simi- 


DOCTRINE OF NECESSITY EXAMINED 


201 


larities and comparative characters, which appeal to our 
intelligence as its cousins, and call upon us for a reason. 
Finally, there is consciousness, feeling, a patent fact enough, 
but a very inconvenient one to the mechanical philosopher. 

Thirdly, the necessitarian may say that chance is not a 
vera causa , that we cannot know positively there is any 
such element in the universe. But the doctrine of the vera 
causa has nothing to do with elementary conceptions. 
Pushed to that extreme, it at once cuts off belief in the 
existence of a material universe; and without that necessi¬ 
tarianism could hardly maintain its ground. Besides, va¬ 
riety is a fact which must be admitted; and the theory of 
chance merely consists in supposing this diversification does 
not antedate all time. Moreover, the avoidance of hy¬ 
potheses involving causes nowhere positively known to act 
— is only a recommendation of logic, not a positive com¬ 
mand. It cannot be formulated in any precise terms with¬ 
out at once betraying its untenable character, — I mean as 
rigid rule, for as a recommendation it is wholesome enough. 

I believe I have thus subjected to fair examination all 
the important reasons for adhering to the theory of uni¬ 
versal necessity, and have shown their nullity. I earnestly 
beg that whoever may detect any flaw in my reasoning will 
point it out to me, either privately or publicly; for if I am 
wrong, it much concerns me to be set right speedily. If 
my argument remains unrefuted, it will be time, I think, to 
doubt the absolute truth of the principle of universal law; 
and when once such a doubt has obtained a living root in 
any man’s mind, my cause with him, I am persuaded, is 
gained. 


III. THE LAW OF MIND 1 


In an article published in The Monist for January, 1891, 

I endeavored to show what ideas ought to form the warp 
of a system of philosophy, and particularly emphasized 
that of absolute chance. In the number of April, 1892, I 
argued further in favor of that way of thinking, which it 
will be convenient to christen tychism (from tvx *?, chance). 
A serious student of philosophy will be in no haste to 
accept or reject this doctrine; but he will see in it one of 
the chief attitudes which speculative thought may take, 
feeling that it is not for an individual, nor for an age, to 
pronounce upon a fundamental question of philosophy. 
That is a task for a whole era to work out. I have begun 
by showing that tychism must give birth to an evolutionary 
cosmology, in which all the regularities of nature and of 
mind are regarded as products of growth, and to a Schelling- 
fashioned idealism which holds matter to be mere specialized 
and partially deadened mind. I may mention, for the bene- 
fit of those who are curious in studying mental biographies, 
that I was born and reared in the neighborhood of Concord, 
— I mean in Cambridge, — at the time when Emerson, 
Hedge, and their friends were disseminating the ideas that 
they had caught from Schelling, and Schelling from Plotinus, 
from Boehm, or from God knows what minds stricken with 
the monstrous mysticism of the East. But the atmosphere 

1 The Monist, July, 1892. 

202 


THE LAW OF MIND 


203 


of Cambridge held many an antiseptic against Concord 
transcendentalism; and I am not conscious of having con¬ 
tracted any of that virus. Nevertheless, it is probable that 
some cultured bacilli, some benignant form of the disease 
was implanted in my soul, unawares, and that now, after 
long incubation, it comes to the surface, modified by mathe¬ 
matical conceptions and by training in physical investiga¬ 
tions. 

The next step in the study of cosmology must be to ex¬ 
amine the general law of mental action. In doing this, I 
shall for the time drop my tychism out of view, in order to 
allow a free and independent expansion to another con¬ 
ception signalized in my first Monist paper as one of the 
most indispensable to philosophy, though it was not there 
dwelt upon; I mean the idea of continuity. The tendency 
to regard continuity, in the sense in which I shall define it, 
as an idea of prime importance in philosophy may con¬ 
veniently be termed synechism. The present paper is in¬ 
tended chiefly to show what synechism is, and what it leads 
to. I attempted, a good many years ago, to develop this 
doctrine in the Journal of Speculative Philosophy (Vol. II.); 
but I am able now to improve upon that exposition, in which 
I was a little blinded by nominalistic prepossessions. I 
refer to it, because students may possibly find that some 
points not sufficiently explained in the present paper are 
cleared up in those earlier ones. 

WHAT THE LAW IS 

Logical analysis applied to mental phenomena shows that 
there is but one law of mind, namely, that ideas tend to 


204 


LOVE AND CHANCE 


spread continuously and to affect certain others which stand 


to them in a peculiar relation of affectibility. In this 


spreading they lose intensity, and especially the power of 
affecting others, but gain generality and become welded with 



I set down this formula at the beginning, for convenience; 
and now proceed to comment upon it. 


INDIVIDUALITY OF IDEAS 


We are accustomed to speak of ideas as reproduced, as 
passed from mind to mind, as similar or dissimilar to one 
another, and, in short, as if they were substantial things; 
nor can any reasonable objection be raised to such expres¬ 
sions. But taking the word “ idea ” in the sense of an 
event in an individual consciousness, it is clear that an idea 
once past is gone forever, and any supposed recurrence of 
it is another idea. These two ideas are not present in the 
same state of consciousness, and therefore cannot possibly 
be compared. To say, therefore, that they are similar can 
only mean that an occult power from the depths of the soul 
forces us to connect them in our thoughts after they are * 
both no more. We may note, here, in passing, that of the 
two generally recognized principles of association, contiguity 
and similarity, the former is a connection due to a power 
without, the latter a connection due to a power within. 

But what can it mean to say that ideas wholly past are 
thought of at all, any longer? They are utterly unknow¬ 
able. What distinct meaning can attach to saying that an 
idea in the past in any way affects an idea in the future, 
from which it is completely detached? A phrase between 


THE LAW OF MIND 


205 

the assertion and the denial of which there can in no case 
be any sensible difference is mere gibberish. 

I will not dwell further upon this point, because it is a 
commonplace of philosophy. 

CONTINUITY OF IDEAS 

We have here before us a question of difficulty, analogous 
to the question of nominalism and realism. But when once 
it has been clearly formulated, logic leaves room for one 
answer only. How can a past idea be present? Can it 
be present vicariously? To a certain extent, perhaps; but 
not merely so; for then the question would arise how the 
past idea can be related to its vicarious representation. 
The relation, being between ideas, can only exist in some 
consciousness: now that past idea was in no consciousness 
but that past consciousness that alone contained it; and 
that did not embrace the vicarious idea. 

Some minds will here jump to the conclusion that a past 
idea cannot in any sense be present. But that is hasty 
and illogical. How extravagant, too, to pronounce our 
whole knowledge of the past to be mere delusion! Yet it 
would seem that the past is as completely beyond the 
bounds of possible experience as a Kantian thing-in-itself. 

How can a past idea be present? Not vicariously. Then, 
only by direct perception. In other words, to be present, 
it must be ipso facto present. That is, it cannot be wholly 
past; it can only be going, infinitesimally past, less past 
than any assignable past date. We are thus brought to 
the conclusion that the present is connected with the past 
by r series of real infinitesimal steps. 


206 


LOVE AND CHANCE 


It has already been suggested by psychologists that con" 
sciousness necessarily embraces an interval of time. But 
if a finite time be meant, the opinion is not tenable. If the 
sensation that precedes the present by half a second were 
still immediately before me, then, on the same principle 
the sensation preceding that would be immediately present, 
and so on ad infinitum. Now, since there is a time, say a 
year, at the end of which an idea is no longer ipso facto 
present, it follows that this is true of any finite interval, 
however short. 

But yet consciousness must essentially cover an interval 
of time; for if it did not, we could gain no knowledge of 
time, and not merely no veracious cognition of it, but no 
conception whatever. We are, therefore, forced to say 
that we are immediately conscious through an infinitesimal 
interval of time. 

This is all that is requisite. For, in this infinitesimal 
interval, not only is consciousness continuous in a subjec¬ 
tive sense, that is, considered as a subject or substance 
having the attribute of duration; but also, because it is 
immediate consciousness, its object is ipso facto continuous. 
In fact, this infinitesimally spread-out consciousness is a 
direct feeling of its contents as spread out. This will be 
further elucidated below. In an infinitesimal interval we 
directly perceive the temporal sequence of its beginning, 
middle, and end, — not, of course, in the way of recogni¬ 
tion, for recognition is only of the past, but in the way of 
immediate feeling. Now upon this interval follows another, 
whose beginning is the middle of the former, and whose 
middle is the end of the former. Here, we have an im- 


THE LAW OF MIND 


207 


mediate perception of the temporal sequence of its begin¬ 
ning, middle, and end, or say of the second, third, and 
fourth instants. From these two immediate perceptions, 
we gain a mediate, or inferential, perception of the relation 
of all four instants. This mediate perception is objectively, 
or as to the object represented, spread over the four in¬ 
stants; but subjectively, or as itself the subject of duration, 
it is completely embraced in the second moment. (The 
reader will observe that I use the word instant to mean a 
point of time, and moment to mean an infinitesimal dura¬ 
tion.) If it is objected that, upon the theory proposed, 
we must have more than a mediate perception of the succes¬ 
sion of the four instants, I grant it; for the sum of the two 
infinitesimal intervals is itself infinitesimal, so that it is 
immediately perceived. It is immediately perceived in the 
whole interval, but only mediately perceived in the last two- 
thirds of the interval. Now, let there be an indefinite 
succession of these inferential acts of comparative percep¬ 
tion; and it is plain that the last moment will contain ob¬ 
jectively the whole series. Let there be, not merely an 
indefinite succession, but a continuous flow of inference 
through a finite time; and the result will be a mediate ob¬ 
jective consciousness of the whole time in the last moment. 
In this last moment, the whole series will be recognized, 
or known as known before, except only the last moment, 
which of course will be absolutely unrecognizable to itself. 
Indeed, even this last moment will be recognized like the 
rest, or, at least, be just beginning to be so. There is a 
little elenchus , or appearance of contradiction, here, which 
the ordinary logic of reflection quite suffices to resolve. 


208 


LOVE AND CHANCE 


INFINITY AND CONTINUITY, IN GENERAL 

Most of the mathematicians who during the last two 
generations have treated the differential calculus have been 
of the opinion that an infinitesimal quantity is an absurdity; 
although, with their habitual caution, they have often added 
“ or, at any rate, the conception of an infinitesimal is so 
difficult, that we practically cannot reason about it with 
confidence and security.” Accordingly, the doctrine of 
limits has been invented to evade the difficulty, or, as some 
say, to explain the signification of the word “ infinitesimal.” 
This doctrine, in one form or another, is taught in all the 
text-books, though in some of them only as an alternative 
view of the matter; it answers well enough the purposes of 
calculation, though even in that application it has its 
difficulties. 

The illumination of the subject by a strict notation for 
the logic of relatives had shown me clearly and evidently 
that the idea of an infinitesimal involves no contradiction, 
before I became acquainted with the writings of Dr. Georg 
Cantor (though many of these had already appeared in the 
Mathematische Annalen and in Bor char dVs Journal, if not 
yet in the Acta Mathematica, all mathematical journals of 
the first distinction), in which the same view is defended 
with extraordinary genius and penetrating logic. 

The prevalent opinion is that finite numbers are the only 
ones that we can reason about, at least, in any ordinary 
mode of reasoning, or, as some authors express it, they are 
the only numbers that can be reasoned about mathemati¬ 
cally. But this is an irrational prejudice. I long ago 



THE LAW OF MIND 


209 


showed that finite collections are distinguished from infinite 
ones only by one circumstance and its consequences, namely, 
that to them is applicable a peculiar and unusual mode of 
reasoning called by its discoverer, De Morgan, the “ syl¬ 
logism of transposed quantity.” 

Balzac, in the introduction of his Physiologie du manage, 
remarks that every young Frenchman boasts of having se¬ 
duced some Frenchwoman. Now, as a woman can only be 
seduced once, and there are no more Frenchwomen than 
Frenchmen, it follows, if these boasts are true, that no 
French women escape seduction. If their number be 
finite, the reasoning holds. But since the population is con¬ 
tinually increasing, and the seduced are on the average 
younger than the seducers, the conclusion need not be true. 
In like manner, De Morgan, as an actuary, might have 
argued that if an insurance company pays to its insured on 
an average more than they have ever paid it, including 
interest, it must lose money. But every modern actuary 
would see a fallacy in that, since the business is continually 
on the increase. But should war, or other cataclysm, cause 
the class of insured to be a finite one, the conclusion would 
turn out painfully correct, after all. The above two reason¬ 
ings are examples of the syllogism of transposed quantity. 

The proposition that finite and infinite collections are 
distinguished by the applicability to the former of the syl¬ 
logism of transposed quantity ought to be regarded as the 
basal one of scientific arithmetic. 

If a person does not know how to reason logically, and 
I must say that a great many fairly good mathematicians, 

yea, distinguished ones, — fall under this category, but 



2 10 


LOVE AND CHANCE 


simply uses a rule of thumb in blindly drawing inferences 
like other inferences that have turned out well, he will, of 
course, be continually falling into error about infinite num¬ 
bers. The truth is such people do not reason, at all. But 
for the few who do reason, reasoning about infinite numbers 
is easier than about finite numbers, because the complicated 
syllogism of transposed quantity is not called for. For 
example, that the whole is greater than its part is not an 
axiom, as that eminently bad reasoner, Euclid, made it to 
be. It is a theorem readily proved by means of a syllogism 
of transposed quantity, but not otherwise. Of finite collec¬ 
tions it is true, of infinite collections false. Thus, a part 
of the whole numbers are even numbers. Yet the even 
numbers are no fewer than all the numbers; an evident 
proposition since if every number in the whole series of 
whole numbers be doubled, the result will be the series of 
even numbers. 

1, 2, 3, 4, 5, 6, etc. 

2, 4, 6, 8, io, 12, etc. 

So for every number there is a distinct even number. In 
fact, there are as many distinct doubles of numbers as there 
are of distinct numbers. But the doubles of numbers are 
all even numbers. 

In truth, of infinite collections there are but two grades 
of magnitude, the endless and the innumerable. Just as a 
finite collection is distinguished from an infinite one by the 
applicability to it of a special mode of reasoning, the syllo¬ 
gism of transposed quantity, so, as I showed in the paper 
last referred to, a numerable collection is distinguished from 
an innumerable one by the applicability to it of a certain 


THE LAW OF MIND 


211 


mode of reasoning, the Fermatian inference, or, as it is 
sometimes improperly termed, “ mathematical induction.” 

As an example of this reasoning, Euler’s demonstration 
of the binomial theorem for integral powers may be given. 
The theorem is that (x + y) n , where n is a whole number, 
may be expanded into the sum of a series of terms of which 
the first is x n y° and each of the others is derived from the 
next preceding by diminishing the exponent of x by i and 
multiplying by that exponent and at the same time increas¬ 
ing the exponent of y by i and dividing by that increased 
exponent. Now, suppose this proposition to be true for a 
certain exponent, n = M , then it must also be true for 
n= M + i. For let one of the terms in the expansion of 
(x + y) M be written A x p y q . Then, this term with the two 
following will be 


A x p y q + A 


p—1 g+l 

x y + A 


p — I P-2 q+ 2 

x y 


q + I " ' q + i q + 2 

Now, when (x + y) M is multiplied by x + y to give (x + y) u+1 , 
we multiply first by x and then by y instead of by x and add 
the two results. When we multiply by x, the second of the 
above three terms will be the only one giving a term involv¬ 
ing x p y 3+1 and the third will be the only one giving a term in 
a nd w r hen we multiply by y the first will be the only 
term giving a term in x p y q+1 , and the second will be the only 
term giving a term in x?~ l y q+2 . Hence, adding like terms, we 
find that the coefficient of x p y q+1 in the expansion of (x + y ) u+1 
will be the sum of the coefficients of the first two of the above 
three terms, and that the coefficient of x p ~ l y q + 2 will be the 
sum of the coefficients of the last two terms. Hence, two 
successive terms in the expansion of (x -f y) MH will be 





212 


LOVE AND CHANCE 


|~i H ——1 x v y q+l + A Pi - 4 - - 1 x 

L ^+ I J ? + I L <7+2j 


q + i J " ' q + 

= A t±JL±J // +1 + A » 


-1 3+2 

y 


< 7+2 

p p—i fl+2 


£ 


g +i ' ' ^ + i ^+2 

It is, thus, seen that the succession of terms follows the rule. 
Thus if any integral power follows the rule, so also does 
the next higher power. But the first power obviously 
follows the rule. Hence, all powers do so. 

Such reasoning holds good of any collection of objects 
capable of being ranged in a series which though it may be 
endless, can be numbered so that each member of it re¬ 
ceives a definite integral number. For instance, all the 
whole numbers constitute such a numerable collection. 
Again, all numbers resulting from operating according to 
any definite rule with any finite number of whole num¬ 
bers form such a collection. For they may be arranged 
in a series thus. Let F be the symbol of operation. First 
operate on i, giving F (i). Then, operate on a second i, 
giving F(i,i). Next, introduce 2, giving 3rd, F(2); 4th 
F(2,i); 5th, F(i,2); 6th, F(2,2). Next use a third vari¬ 
able giving 7th, F(i,i,i); 8th, F(2,i,i); 9th, F(i,2*i); 
10th, F( 2 , 2 ,i); nth, F(i,i, 2 ); 12th, F(2,i,2); 13th, 
F( 1,2,2); 14th, F(2,2,2). Next introduce 3, and so on, 
alternately introducing new variables and new figures; and 
in this way it is plain that every arrangement of integral 
values of the variables will receive a numbered place in 
the series. 2 

The class of endless but numerable collections (so called 
because they can be so ranged that to each one corresponds 

2 This proposition is substantially the same as a theorem of Cantor, 
though it is enunciated in a much more general form. 








THE LAW OF MIND 


213 


a distinct whole number) is very large. But there are 
collections which are certainly innumerable. Such is the 
collection of all numbers to which endless series of decimals 
are capable of approximating. It has been recognized since 
the time of Euclid that certain numbers are surd or incom¬ 
mensurable, and are not exactly expressible by any finite 
series of decimals, nor by a circulating decimal. Such is 

the ratio of the circumference of a circle to its diameter, 

* 

which we know is nearly 3.1415926. The calculation of 
this number has been carried to over 700 figures without 
the slightest appearance of regularity in their sequence. 
The demonstrations that this and many other numbers are 
incommensurable are perfect. That the entire collection of 
incommensurable numbers is innumerable has been clearly 
proved by Cantor. I omit the demonstration; but it is easy 
to see that to discriminate one from some other would, in 
general, require the use of an endless series of numbers. 
Now if they cannot be exactly expressed and discriminated, 
clearly they cannot be ranged in a linear series. 

It is evident that there are as many points on a line or in 
an interval of time as there are of real numbers in all. 
These are, therefore, innumerable collections. Many mathe¬ 
maticians have incautiously assumed that the points on a 
surface or in a solid are more than those on a line. But 
this has been refuted by Cantor. Indeed, it is obvious that 
for every set of values of coordinates there is a single dis¬ 
tinct number. Suppose, for instance, the values of the co¬ 
ordinates all lie between o and + 1. Then if we compose 
a number by putting in the first decimal place the first figure 
of the first coordinate, in the second the first figure of the 


214 


LOVE AND CHANCE 


second coordinate, and so on, and when the first figures are 
all dealt out go on to the second figures in like manner, 
it is plain that the values of the coordinates can be read off 
from the single resulting number, so that a triad or tetrad of 
numbers, each having innumerable values, has no more 
values than a single incommensurable number. 

Were the number of dimensions infinite, this would fail; 
and the collection of infinite sets of numbers having each 
innumerable variations, might, therefore, be greater than 
the simple innumerable collection, and might be called 
endlessly infinite. The single individuals of such a collec¬ 
tion could not, however, be designated, even approximately, 
so that this is indeed a magnitude concerning which it would 
be possible to reason only in the most general way, if at all. 

Although there are but two grades of magnitudes of in¬ 
finite collections, yet when certain conditions are imposed 
upon the order in which individuals are taken, distinctions 
of magnitude arise from that cause. Thus, if a simply 
endless series be doubled by separating each unit into two 
parts, the successive first parts and also the second parts 
being taken in the same order as the units from which they 
are derived, this double endless series will, so long as it is 
taken in that order, appear as twice as large as the original 
series. In like manner the product of two innumerable 
collections, that is, the collection of possible pairs composed 
of one individual of each, if the order of continuity is to be 
maintained, is, by virtue of that order, infinitely greater 
than either of the component collections. 

We now come to the difficult question. What is con¬ 
tinuity? Kant confounds it with infinite divisibility, saying 



THE LAW OF MIND 


215 

that the essential character of a continuous series is that 
between any two members of it a third can always be found. 
This is an analysis beautifully clear and definite; but un¬ 
fortunately, it breaks down under the first test. For ac¬ 
cording to this, the entire series of rational fractions ar¬ 
ranged in the order of their magnitude, would be an infinite 
series, although the rational fractions are numerable, while 
the points of a line are innumerable. Nay, worse yet, if 
from that series of fractions any two with all that lie be¬ 
tween them be excised, and any number of such finite gaps 
be made, Kant’s definition is still true of the series, though 
it has lost all appearance of continuity. 

Cantor defines a continuous series as one which is con¬ 
catenated and perfect. By a concatenated series, he means 
such a one that if any two points are given in it, and any 
finite distance, however small, it is possible to proceed from 
the first point to the second through a succession of points 
of the series each at a distance from the preceding one less 
than the given distance. This is true of the series of ra¬ 
tional fractions ranged in the order of their magnitude. 
By a perfect series, he means one which contains every 
point such that there is no distance so small that this point 
has not an infinity of points of the series within that dis¬ 
tance of it. This is true of the series of numbers between 
o and 1 capable of being expressed by decimals in which 
only the digits o and 1 occur. 

It must be granted that Cantor’s definition includes every 
series that is continuous; nor can it be objected that it 
includes any important or indubitable case of a series not 

i 

continuous. Nevertheless, it has some serious defects. In 


216 


LOVE AND CHANCE 


the first place, it turns upon metrical considerations; while 
the distinction between a continuous and a discontinuous 
series is manifestly non-metrical. In the next place, a per¬ 
fect series is defined as one containing “ every point ” of 
a certain description. But no positive idea is conveyed of 
what all the points are: that is definition by negation, and 
cannot be admitted. If that sort of thing were allowed, 
it would be very easy to say, at once, that the continuous 
linear series of points is one which contains every point of 
the line between its extremities. Finally, Cantor’s defini¬ 
tion does not convey a distinct notion of what the compo¬ 
nents of the conception of continuity are. It ingeniously 
wraps up its properties in two separate parcels, but does not 
display them to our intelligence. 

Kant’s definition expresses one simple property of a con¬ 
tinuum; but it allows of gaps in the series. To mend the 
definition, it is only necessary to notice how these gaps can 
occur. Let us suppose, then, a linear series of points ex¬ 
tending from a point, A, to a point, B, having a gap from 
B to a third point, C, and thence extending to a final limit, 
D; and let us suppose this series conforms to Kant’s defini¬ 
tion. Then, of the two points, B and C, one or both must 
be excluded from the series; for otherwise, by the definition, 
there would be points between them. That is, if the series 
contains C, though it contains all the points up to B, it can¬ 
not contain B. What is required, therefore, is to state in 
non-metrical terms that if a series of points up to a limit 
is included in a continuum the limit is included. It may 
be remarked that this is the property of a continuum to 
which Aristotle’s attention seems to have been directed 


THE LAW OF MIND 


217 


when he defines a continuum as something whose parts 
have a common limit. The property may be exactly stated 
as follows: If a linear series of points is continuous be¬ 
tween two points, A and D, and if an endless series of 
points be taken, the first of them between A and D and 
each of the others between the last preceding one and D, 
then there is a point of the continuous series between all 
that endless series of points and D, and such that every 
other point of which this is true lies between this point 
and D . For example, take any number between o and 1, 
as 0.1; then, any number between 0.1 and 1, as o.n; then 
any number between o.n and 1, as o.m; and so on, with¬ 
out end. Then, because the series of real numbers be¬ 
tween o and 1 is continuous, there must be a least real 
number, greater than every number of that endless series. 
This property, which may be called the Aristotelicity of the 
series, together with Kant’s property, or its Kanticity, 
completes the definition of a continuous series. 

The property of Aristotelicity may be roughly stated 
thus: a continuum contains the end point belonging to every 
endless series of points which it contains. An obvious 
corollary is that every continuum contains its limits. But 
in using this principle it is necessary to observe that a series 
may be continuous except in this, that it omits one or both 
of the limits. 

Our ideas will find expression more conveniently if, in¬ 
stead of points upon a line, we speak of real numbers. 
Every real number is^ in one sense, the limit of a series, 
for it can be indefinitely approximated to. Whether every 
real number is a limit of a regular series may perhaps be 


218 


LOVE AND CHANCE 


open to doubt. But the series referred to in the definition 
of Aristotelicity must be understood as including all series 
whether regular or not. Consequently, it is implied that 
between any two points an innumerable series of points 
can be taken. 

Every number whose expression in decimals requires but 
a finite number of places of decimals is commensurable. 
Therefore, incommensurable numbers suppose an infinitieth 
place of decimals. The word infinitesimal is simply the 
Latin form of infinitieth; that is, it is an ordinal formed 
from infinitum , as centesimal from centum . Thus, con¬ 
tinuity supposes infinitesimal quantities. There is nothing 
contradictory about the idea of such quantities. In adding 
and multiplying them the continuity must not be broken up, 
and consequently they are precisely like any other quan¬ 
tities, except that neither the syllogism of transposed 
quantity, nor the Fermatian inference applies to them. 

If A is a finite quantity and i an infinitesimal, then in a 
certain sense we may write A + i = A. That is to say, 
this is so for all purposes of measurement. But this prin¬ 
ciple must not be applied except to get rid of all the terms 
in the highest order of infinitesimals present. As a mathe¬ 
matician, I prefer the method of infinitesimals to that of 
limits, as far easier and less infested with snares. Indeed, 
the latter, as stated in some books, involves propositions 
that are false; but this is not the case with the forms of 
the method used by Cauchy, Duhamel, and others. As they 
understand the doctrine of limits, it involves the notion of 
continuity, and, therefore, contains in another shape the 
very same ideas as the doctrine of infinitesimals. 


THE LAW OF MIND 


219 


Let us now consider an aspect of the Aristotelical prin¬ 
ciple which is particularly important in philosophy. Sup¬ 
pose a surface to be part red and part blue; so that every 
point on it is either red or blue, and, of course, no part 
can be both red and blue. What, then, is the color of the 
boundary line between the red and the blue? The answer 
is that red or blue, to exist at all, must be spread over a 
surface; and the color of the surface is the color of the 
surface in the immediate neighborhood of the point. I 
purposely use a vague form of expression. Now, as the 
parts of the surface in the immediate neighborhood of any 
ordinary point upon a curved boundary are half of them 
red and half blue, it follows that the boundary is half red 
and half blue. In like manner, we find it necessary to 
hold that consciousness essentially occupies time; and what 
is present to the mind at any ordinary instant, is what is 
present during a moment in which that instant occurs. 
Thus, the present is half past and half to come. Again, 
the color of the parts of a surface at any finite distance 
from a point, has nothing to do with its color just at that 
point; and, in the parallel, the feeling at any finite interval 
from the present has nothing to do with the present feeling, 
except vicariously. Take another case: the velocity of a 
particle at any instant of time is its mean velocity during 
an infinitesimal instant in which that time is contained. 
Just so my immediate feeling is my feeling through an in¬ 
finitesimal duration containing the present instant. 



220 


LOVE AND CHANCE 


ANALYSIS OF TIME 

One of the most marked features about the law of mind 
is that it makes time to have a definite direction of flow 
from past to future. The relation of past to future is, in 
reference to the law of mind, different from the relation of 
future to past. This makes one of the great contrasts be¬ 
tween the law of mind and the law of physical force, where 
there is no more distinction between the two opposite direc¬ 
tions in time than between moving northward and moving 
southward. 

In order, therefore, to analyze the law of mind, we must 
begin by asking what the flow of time consists in. Now, 
we find that in reference to any individual state of feeling, 
all others are of two classes, those which affect this one 
(or have a tendency to affect it, and what this means we 
shall inquire shortly), and those which do not. The present 
is affectible by the past but not by the future. 

Moreover, if state A is affected by state B, and state B 
by state C, then A is affected by state C, though not so much 
so. It follows, that if A is affectible by B, B is not affectible 
by A. 

If, of two states, each is absolutely unaffectible by the 
other, they are to be regarded as parts of the same state. 
They are contemporaneous. 

To say that a state is between two states means that it 
affects one and is affected by the other. Between any two 
states in this sense lies an innumerable series of states af¬ 
fecting one another; and if a state lies between a given state 
and any other state which can be reached by inserting 


THE LAW OF MIND 


221 


states between this state and any third state, these inserted 
states not immediately affecting or being affected by either, 
then the second rate mentioned, immediately affects or is 
affected by the first, in the sense that in the one the other is 
ipso facto present in a reduced degree. 

These propositions involve a definition of time and of its 
flow. Over and above this definition they involve a doc¬ 
trine, namely, that every state of feeling is affectible by 
every earlier state. 

THAT FEELINGS HAVE INTENSIVE CONTINUITY 

Time with its continuity logically involves some other 
kind of continuity than its own. Time, as the universal 
form of change, cannot exist unless there is something to 
undergo change, and to undergo a change continuous in 
time, there must be a continuity of changeable qualities. 
Of the continuity of intrinsic qualities of feeling we can now 
form but a feeble conception. The development of the 
human mind has practically extinguished all feelings, ex¬ 
cept a few sporadic kinds, sound, colors, smells, warmth, 
etc., which now appear to be disconnected and disparate. 
In the case of colors, there is a tridimensional spread of 
feelings. Originally, all feelings may have been connected 
in the same way, and the presumption is that the number 
of dimensions was endless. For development essentially 
involves a limitation of possibilities. But given a number 
of dimensions of feeling, all possible varieties are obtainable 
by varying the intensities of the different elements. Accord¬ 
ingly, time logically supposes a continuous range of in¬ 
tensity in feeling. It follows, then, from the definition of 


222 


LOVE AND CHANCE 


continuity, that when any particular kind of feeling is 
present, an infinitesimal continuum of all feelings differing 
infinitesimally from that is present. 

THAT FEELINGS HAVE SPATIAL EXTENSION 

Consider a gob of protoplasm, say an amoeba or a slime- 
mould. It does not differ in any radical way from the 
contents of a nerve-cell, though its functions may be less 
specialized. There is no doubt that this slime-mould, or 
this amoeba, or at any rate some similar mass of protoplasm 
feels. That is to say, it feels when it is in its excited con¬ 
dition. But note how it behaves. When the whole is 
quiescent and rigid, a place upon it is irritated. Just at 
this point, an active motion is set up, and this gradually 
spreads to other parts. In this action, no unity nor relation 
to a nucleus, or other unitary organ can be discerned. It 
is a mere amorphous continuum of protoplasm, with feeling 
passing from one part to another. Nor is there anything 
like a wave-motion. The activity does not advance to 
new parts, just as fast as it leaves old parts. Rather, in 
the beginning, it dies out at a slower rate than that at which 
it spreads. And while the process is going on, by exciting 
the mass at another point, a second quite independent state 
of excitation will be set up. In some places, neither ex¬ 
citation will exist, in others each separately, in still other 
places, both effects will be added together. Whatever there 
is in the whole phenomenon to make us think there is feel¬ 
ing in such a mass of protoplasm, — feeling, but plainly no 
personality, — goes logically to show that that feeling has 
a subjective, or substantial, spatial extension, as the excited 


THE LAW OF MIND 223 

t 

state has. This is, no doubt, a difficult idea to seize, for 
the reason that it is a subjective, not an objective, extension. 
It is not that we have a feeling of bigness; though Pro¬ 
fessor James, perhaps rightly, teaches that we have. It is 
that the feeling, as a subject of inhesion, is big. Moreover, 
our own feelings are focused in attention to such a degree 
that we are not aware that ideas are not brought to an ab¬ 
solute unity; just as nobody not instructed by special ex¬ 
periment has any idea how very, very little of the field of 
vision is distinct. Still, we all know how the attention 
wanders about among our feelings; and this fact shows 
that those feelings that are not co-ordinated in attention 
have a reciprocal externality, although they are present at 
the same time. But we must not tax introspection to make 
a phenomenon manifest which essentially involves exter¬ 
nality. 

Since space is continuous, it follows that there must be 
an immediate community of feeling between parts of mind 
infinitesimally near together. Without this, I believe it 
would have been impossible for minds external to one 
another, ever to become co-ordinated, and equally impossi¬ 
ble for any coordination to be established in the action of 
the nerve-matter of one brain. 

AFFECTIONS OF IDEAS 

But we are met by the question what is meant by saying 
that one idea affects another. The unravelment of this 
problem requires us to trace out phenomena a little further. 

Three elements go to make up an idea.' The first is its 
intrinsic quality as a feeling. The second is the energy 


224 


LOVE AND CHANCE 


with which it affects other ideas, an energy which is infinite 
in the here-and-nowness of immediate sensation, finite and 
relative in the recency of the past. The third element is 
the tendency of an idea to bring along other ideas with it. 

As an idea spreads, its power of affecting other ideas gets 
rapidly reduced; but its intrinsic quality remains nearly 
unchanged. It is long years now since I last saw a cardinal 
in his robes; and my memory of their color has become 
much dimmed. The color itself, however, is not remem¬ 
bered as dim. I have no inclination to call it a dull red. 
Thus, the intrinsic quality remains little changed; yet 
more accurate observation will show a slight reduction of 
it. The third element, on the other hand, has increased. 
As well as I can recollect, it seems to me the cardinals I 
used to see wore robes more scarlet than vermillion is, 
and highly luminous. Still, I know the color commonly 
called cardinal is on the crimson side of vermillion and of 
quite moderate luminosity, and the original idea calls up 
so many other hues with it, and asserts itself so feebly, that 
I am unable any longer to isolate it. 

A finite interval of time generally contains an innumer¬ 
able series of feelings; and when these become welded to¬ 
gether in association, the result is a general idea. For we 
have just seen how by continuous spreading an idea be¬ 
comes generalised. 

The first character of a general idea so resulting is that 
it is living feeling. A continuum of this feeling, infinitesi¬ 
mal in duration, but still embracing innumerable parts, 
and also, though infinitesimal, entirely unlimited, is im¬ 
mediately present. And in its absence of boundedness a 


THE LAW OF MIND 


225 


vague possibility of more than is present is directly felt. 

Second, in the presence of this continuity of feeling, 
nominalistic maxims appear futile. There is no doubt 
about one idea affecting another, when we can directly 
perceive the one gradually modified and shaping itself into 
the other. Nor can there any longer be any difficulty about 
one idea resembling another, when we can pass along the 
continuous field of quality from one to the other and back 
again to the point which we had marked. 



Third, consider the insistency of an idea. The insistency 
of a past idea with reference to the present is a quantity 
which is less the further back that past idea is, and rises to 
infinity as the past idea is brought up into coincidence with 
the present. Here we must make one of those inductive 
applications of the law of continuity which have produced 







226 


LOVE AND CHANCE 


such great results in all the positive sciences. We must 
extend the law of insistency into the future. Plainly, the 
insistency of a future idea with reference to the present is a 
quantity affected by the minus sign; for it is the present 
that affects the future, if there be any effect, not the future 
that affects the present. Accordingly, the curve of insis¬ 
tency is a sort of equilateral hyperbola. (See the figure.) 
Such a conception is none the less mathematical, that its 
quantification cannot now be exactly specified. 

Now consider the induction which we have here been led 
into. This curve says that feeling which has not yet 
emerged into immediate consciousness is already affectible 
and already affected. In fact, this is habit, by virtue of 
which an idea is brought up into present consciousness by 
a bond that had already been established between it and 
another idea while it was still in juturo. 

We can now see what the affection of one idea by an¬ 
other consists in. It is that the affected idea is attached 
as a logical predicate to the affecting idea as subject. So 
when a feeling emerges into immediate consciousness, it 
always appears as a modification of a more or less general 
object already in the mind. The word suggestion is well 
adapted to expressing this relation. The future is suggested 
by, or rather is influenced by the suggestions of, the past. 

IDEAS CANNOT BE CONNECTED EXCEPT BY CONTINUITY 

That ideas can nowise be connected without continuity 
is sufficiently evident to one who reflects upon the matter. 
But still the opinion may be entertained that after con¬ 
tinuity has once made the connection of ideas possible, 


THE LAW OF MIND 227 

then they may get to be connected in other modes than 
through continuity. Certainly, I cannot see how anyone 
can deny that the infinite diversity of the universe, which 
we call chance, may bring ideas into proximity which are 
not associated in one general idea. It may do this many 
times. But then the law of continuous spreading will pro- 
duce a mental association; and this I suppose is an abridged 
statement of the way the universe has been evolved. But 
if I am asked whether a blind dvdyKTj cannot bring ideas 
together, first I point out that it would not remain blind. 
There being a continuous connection between the ideas, 
they would infallibly become associated in a living, feeling, 
and perceiving general idea. Next, I cannot see what the 
mustness or necessity of this avayKrj would consist in. 
In the absolute uniformity of the phenomenon, says the 
nominalist. Absolute is well put in; for if it merely hap¬ 
pened so three times in succession, or three million times 
in succession, in the absence of any reason, the coincidence 
could only be attributed to chance. But absolute uni¬ 
formity must extend over the whole infinite future; and it 
is idle to talk of that except as an idea. No; I think we 
can only hold that wherever ideas come together they tend 
to weld into general ideas; and wherever they are generally 
connected, general ideas govern the connection; and these 
general ideas are living feelings spread out. 

MENTAL LAW FOLLOWS THE FORMS OF LOGIC 

The three main classes of logical inference' are Deduction, 
Induction, and Hypothesis. These correspond to three 
chief modes of action of the human soul. In deduction the 


228 


LOVE AND CHANCE 


mind is under the dominion of a habit or association by 
virtue of which a general idea suggests in each case a corre¬ 
sponding reaction. But a certain sensation is seen to in¬ 
volve that idea. Consequently, that sensation is followed 
by that reaction. That is the way the hind legs of a frog, 
separated from the rest of the body, reason, when you 
pinch them. It is the lowest form of psychical manifes¬ 
tation. 

By induction, a habit becomes established. Certain sen¬ 
sations, all involving one general idea, are followed each 
by the same reaction; and an association becomes estab¬ 
lished, whereby that general idea gets to be followed uni¬ 
formly by that reaction. 

Habit is that specialization of the law of mind whereby 
a general idea gains the power of exciting reactions. But 
in order that the general idea should attain all its func¬ 
tionality, it is necessary, also, that it should become sug¬ 
gestible by sensations. That is accomplished by a psychical 
process having the form of hypothetic inference. By hypo¬ 
thetic inference, I mean, as I have explained in other writ¬ 
ings, an induction from qualities. For example, I know 
that the kind of man known and classed as a “ mugwump ” 
has certain characteristics. He has a high self-respect and 
places great value upon social distinction. He laments the 
great part that rowdyism and unrefined good-fellowship 
play in the dealings of American politicians with their con¬ 
stituency. He thinks that the reform which would follow 
from the abandonment of the system by which the dis¬ 
tribution of offices is made to strengthen party organizations 
and a return to the original and essential conception of 


THE LAW OF MIND 


229 


office-filling would be found an unmixed good. He holds 
that monetary considerations should usually be the decisive 
ones in questions of public policy. He respects the prin¬ 
ciple of individualism and of laissez-faire as the greatest 
agency of civilization. These views, among others, I know 
to be obtrusive marks of a “ muyvump .” Now, suppose 
I casually meet a man in a railway-train, and falling into 
conversation find that he holds opinions of this sort; I am 
naturally led to suppose that he is a “ mugwump.” That 
is hypothetic inference. That is to say, a number of readily 
verifiable marks of a mugwump being selected, I find this 
man has these, and infer that he has all the other characters 
which go to make a thinker of that stripe. Or let us sup¬ 
pose that I meet a man of a semi-clerical appearance and 
a sub-pharisaical sniff, who appears to look at things from 
the point of view of a rather wooden dualism. He cites 
several texts of scripture and always with particular atten¬ 
tion to their logical implications; and he exhibits a stern¬ 
ness, almost amounting to vindictiveness, toward evil-doers, 
in general. I readily conclude that he is a minister of a 
certain denomination. Now the mind acts in a way similar 
to this, every time we acquire a power of co-ordinating re¬ 
actions in a peculiar way, as in performing any act requir¬ 
ing skill. Thus, most persons have a difficulty in moving 
the two hands simultaneously and in opposite directions 
through two parallel circles nearly in the medial plane of 
the body. To learn to do this, it is necessary to attend, 
first, to the different actions in different parts of the motion, 
when suddenly a general conception of the action springs 
up and it becomes perfectly easy. We think the motion 



230 


LOVE AND CHANCE 


we are trying to do involves this action, and this, and this. 
Then, the general idea comes which unites all those actions, 
and thereupon the desire to perform the motion calls up 
the general idea. The same mental process is many times 
employed whenever we are learning to speak a language 
or are acquiring any sort of skill. 

Thus, by induction, a number of sensations followed by 
one reaction become united under one general idea followed 
by the same reaction; while by the hypothetic process, a 
number of reactions called for by one occasion get united 
in a general idea which is called out by the same occasion. 
By deduction, the habit fulfils its function of calling out 
certain reactions on certain occasions. 

UNCERTAINTY OF MENTAL ACTION 

The inductive and hypothetic forms of inference are 
essentially probable inferences, not necessary; while deduc¬ 
tion may be either necessary or probable. 

But no mental action seems to be necessary or invariable 
in its character. In whatever manner the mind has reacted 
under a given sensation, in that manner it is the more likely 
to react again; were this, however, an absolute necessity, 
habits would become wooden and ineradicable, and no room 
being left for the formation of new habits, intellectual life 
would come to a speedy close. Thus, the uncertainty of 
the mental law is no mere defect of it, but is on the con¬ 
trary of its essence. The truth is, the mind is not subject 
to “law,” in the same rigid sense that matter is. It only 
experiences gentle forces which merely render it more likely 
to act in a given way than it otherwise would be. There 


THE LAW OF MIND 


2 3 1 


always remains a certain amount of arbitrary spontaneity 
in its action, without which it would be dead. 

Some psychologists think to reconcile the uncertainty of 
reactions with the principle of necessary causation by means 
of the law of fatigue. Truly for a law, this law of fatigue 
is a little lawless. I think it is merely a case of the general 
principle that an idea in spreading loses its insistency. 
Put me tarragon into my salad, when I have not tasted it 
for years, and I exclaim “ What nectar is this! ” But add 
it to every dish I taste for week after week, and a habit of 
expectation has been created; and in thus spreading into 
habit, the sensation makes hardly any more impression upon 
me; or, if it be noticed, it is on a new side from which it 
appears as rather a bore. The doctrine that fatigue is one 
of the primordial phenomena of mind I am much disposed 
to doubt. It seems a somewhat little thing to be allowed 
as an exception to the great principle of mental uniformiza- 
tion. For this reason, I prefer to explain it in the manner 
here indicated, as a special case of that great principle. 
To consider it as something distinct in its nature, certainly 
somewhat strengthens the necessitarian position; but even 
if it be distinct, the hypothesis that all the variety and 
apparent arbitrariness of mental action ought to be ex¬ 
plained away in favor of absolute determinism does not 
seem to me to recommend itself to a sober and sound judg¬ 
ment, which seeks the guidance of observed facts and not 
that of prepossessions. 


232 


LOVE AND CHANCE 


RESTATEMENT OF THE LAW 

Let me now try to gather up all these odds and ends of 
commentary and restate the law of mind, in a unitary way. 

First, then, we find that when we regard ideas from a 
nominalistic, individualistic, sensualistic way, the simplest 
facts of mind become utterly meaningless. That one idea 
should resemble another or influence another, or that one 
state of mind should so much as be thought of in another is, 
from that standpoint, sheer nonsense. 

Second, by this and other means we are driven to per¬ 
ceive, what is quite evident of itself, that instantaneous 
feelings flow together into a continuum of feeling, which 
has in a modified degree the peculiar vivacity of feeling and 
has gained generality. And in reference to such general 
ideas, or continua of feeling, the difficulties about resem¬ 
blance and suggestion and reference to the external, cease 
to have any force. 

Third, these general ideas are not mere words, nor do 
they consist in this, that certain concrete facts will every 
time happen under certain descriptions of conditions; but 
they are just as much, or rather far more, living realities 
than the feelings themselves out of which they are concreted. 
And to say that mental phenomena are governed by law 
does not mean merely that they are describable by a general 
formula; but that there is a living idea, a conscious con¬ 
tinuum of feeling, which pervades them, and to which they 
are docile. 

Fourth, this supreme law, which is the celestial and liv¬ 
ing harmony, does not so much as demand that the special 


THE LAW OF MIND 


233 


ideas shall surrender their peculiar arbitrariness and caprice 
entirely; for that would be self-destructive. It only re¬ 
quires that they shall influence and be influenced by one 
another. 

Fifth, in what measure this unification acts, seems to be 
regulated only by special rules; or, at least, we cannot in 
our present knowledge say how far it goes. But it may 
be said that, judging by appearances, the amount of arbi¬ 
trariness in the phenomena of human minds is neither 
altogether trifling nor very prominent. 

PERSONALITY 

Having thus endeavored to state the law of mind, in gen¬ 
eral, I descend to the consideration of a particular phe¬ 
nomenon which is remarkably prominent in our own con¬ 
sciousnesses, that of personality. A strong light is thrown 
upon this subject by recent observations of double and 
multiple personality. The theory which at one time seemed 
plausible that two persons in one body corresponded to the 
two halves of the brain will, I take it, now be universally 
acknowledged to be insufficient. But that which these 
cases make quite manifest is that personality is some kind 
of co-ordination or connection of ideas. Not much to say, 
this, perhaps. Yet when we consider that, according to the 
principle which we are tracing out, a connection between 
ideas is itself a general idea, and that a general idea is a 
living feeling, it is plain that we have at least taken an ap¬ 
preciable step toward the understanding of personality. 
This personality, like any general idea, is not a thing to 
be apprehended in an instant. It has to be lived in time; 



234 


LOVE AND CHANCE 


nor can any finite time embrace it in all its fullness. Yet 
in each infinitesimal interval it is present and living, though 
specially colored by the immediate feelings of that moment. 
Personality, so far as it is apprehended in a moment, is 
immediate self-consciousness. 

But the word co-ordination implies somewhat more than 
this; it implies a teleological harmony in ideas, and in the 
case of personality this teleology is more than a mere pur¬ 
posive pursuit of a predeterminate end; it is a develop¬ 
mental teleology. This is personal character. A general 
idea, living and conscious now, it is already determinative 
of acts in the future to an extent to which it is not now 
conscious. 

This reference to the future is an essential element of 
personality. Were the ends of a person already explicit, 
there would be no room for development, for growth, for 
life; and consequently there would be no personality. The 
mere carrying out of predetermined purposes is mechanical. 
This remark has an application to the philosophy of religion. 
It is that a genuine evolutionary philosophy, that is, one 
that makes the principle of growth a primordial element 
of the universe, is so far from being antagonistic to the idea 
of a personal creator, that it is really inseparable from that 
idea; while a necessitarian religion is in an altogether false 
position and is destined to become disintegrated. But a 
pseudo-evolutionism which enthrones mechanical law above 
the principle of growth, is at once scientifically unsatis¬ 
factory, as giving no possible hint of how the universe has 
come about, and hostile to all hopes of personal relations 
to God. 


THE LAW OF MIND 


*35 


COMMUNICATION 

Consistently with the doctrine laid down in the beginning 
of this paper, I am bound to maintain that an idea can only 
be affected by an idea in continuous connection with it. 
By anything but an idea, it cannot be affected at all. This 
obliges me to say, as I do say, on other grounds, that what 
we call matt er is not completely dead, but is merely mind 
hide-bound with habits. It still retains the element of 
diversification; and in that diversification there is life. 
When an idea is conveyed from one mind to another, it is 
by forms of combination of the diverse elements of nature, 
say by some curious symmetry, or by some union of a tender 
color with a refined odor. To such forms the law of me¬ 
chanical energy has no application. If they are eternal, 
it is in the spirit they embody; and their origin cannot be 
accounted for by any mechanical necessity. They are em¬ 
bodied ideas; and so only can they convey ideas. Precisely 
how primary sensations, as colors and tones, are excited, 
we cannot tell, in the present state of psychology. But in 
our ignorance, I think that we are at liberty to suppose 
that they arise in essentially the same manner as the other 
feelings, called secondary. As far as sight and hearing 
are in question, we know that they are only excited by vi¬ 
brations of inconceivable complexity; and the chemical 
senses are probably not more simple. Even the least psy¬ 
chical of peripheral sensations, that of pressure, has in its 
excitation conditions which, though apparently simple, are 
seen to be complicated enough when we consider the mole¬ 
cules and their attractions. The principle with which I 


236 


LOVE AND CHANCE 


» 

set out requires me to maintain that these feelings are 
communicated to the nerves by continuity, so that there 
must be something like them in the excitants themselves. 
If this seems extravagant, it is to be remembered that it is 
the sole possible way of reaching any explanation of sen¬ 
sation, which otherwise must be pronounced a general fact, 
absolutely inexplicable and ultimate. Now absolute in¬ 
explicability is a hypothesis which sound logic refuses under 
any circumstances to justify. 

I may be asked whether my theory would be favorable 
or otherwise to telepathy. I have no decided answer to 
give to this. At first sight, it seems unfavorable. Yet 
there may be other modes of continuous connection between 
minds other than those of time and space. 

The recognition by one person of another’s personality 
takes place by means to some extent identical with the means 
by which he is conscious of his own personality. The idea 
of the second personality, which is as much as to say that 
second personality itself, enters within the field of direct 
consciousness of the first person, and is as immediately 
perceived as his ego, though less strongly. At the same 
time, the opposition between the two persons is perceived, 
so that the externality of the second is recognized. 

The psychological phenomena of intercommunication be¬ 
tween two minds have been unfortunately little studied. So 
that it is impossible to say, for certain, whether they are 
favorable to this theory or not. But the very extraordinary 
insight which some persons are able to gain of others from 
indications so slight that it is difficult to ascertain what 
they are, is certainly rendered more comprehensible by the 
view here taken. 


THE LAW OF MIND 


237 


A difficulty which confronts the synechistic philosophy is 
this. In considering personality, that philosophy is forced 
to accept the doctrine of a personal God; but in considering 
communication, it cannot but admit that if there is a per¬ 
sonal God, we must have a direct perception of that person 
and indeed be in personal communication with him. Now, 
if that be the case, the question arises how it is possible that 
the existence of this being should ever have been doubted 
by anybody. The only answer that I can at present make 
is that facts that stand before our face and eyes and stare 
us in the face are far from being, in all cases, the ones most 
easily discerned. That has been remarked from time im¬ 
memorial. 

CONCLUSION 

I have thus developed as well as I could in a little space 
the synechistic philosophy, as applied to mind. I think 
that I have succeeded in making it clear that this doctrine 
gives room for explanations of many facts which without it 
are absolutely and hopelessly inexplicable; and further that 
it carries along with it the following doctrines: 1st, a logi¬ 
cal realism of the most pronounced type; 2nd, objective 
idealism; 3rd, tychism, with its consequent thoroughgoing 
evolutionism. We also notice that the doctrine presents no 
hindrances to spiritual influences, such as some philosophies 
are felt to do. 


IV. MAN’S GLASSY ESSENCE 1 


In The Monist for January, 1891, I tried to show what 
conceptions ought to form the brick and mortar of a phi¬ 
losophical system. Chief among these was that of absolute 
chance for which I argued again in last April’s number. 2 
In July, I applied another fundamental idea, that of con¬ 
tinuity, to the law of mind. Next in order, I have to eluci¬ 
date, from the point of view chosen, the relation between 
the psychical and physical aspects of a substance. 

The first step towards this ought, I think, to be the fram¬ 
ing of a molecular theory of protoplasm. But before doing 
that, it seems indispensable to glance at the constitution 
of matter, in general. We shall, thus, unavoidably make a 
long detour; but, after all, our pains will not be wasted, 
for the problems of the papers that are to follow in the series 
will call for the consideration of the same question. 

All physicists are rightly agreed the evidence is over¬ 
whelming which shows all sensible matter is composed of 
molecules in swift motion and exerting enormous mutual 
attractions, and perhaps repulsions, too. Even Sir William 
Thomson, Lord Kelvin, who wishes to explode action at a 
distance and return to the doctrine of a plenum, not only 
speaks of molecules, but undertakes to assign definite mag- 

1 The Monist, October, 1892. 

2 I am rejoiced to find, since my last paper was printed, that a phil¬ 
osopher as subtle and profound as Dr. Edmund Montgomery has long 
been arguing for the same element in the universe. Other world-renowned 
thinkers, as M. Renouvier and M. Delboeuf, appear to share this opinion. 

238 


MAN’S GLASSY ESSENCE 


239 


nitudes to them. The brilliant Judge Stallo, a man who did 
not always rightly estimate his own qualities in accepting 
tasks for himself, declared war upon the atomic theory in 
a book well worth careful perusal. To the old arguments 
in favor of atoms which he found in Fechner’s monograph, 
he was able to make replies of considerable force, though 
they were not sufficient to destroy those arguments. But 
against modern proofs he made no headway at all. These 
set out from the mechanical theory of heat. Rumford’s 
experiments showed that heat is not a substance. Joule 
demonstrated that it was a form of energy. The heating 
of gases under constant volume, and other facts instanced 
by Rankine, proved that it could not be an energy of strain. 
This drove physicists to the conclusion that it was a mode 
of motion. Then it was remembered that John Bernoulli 
had shown that the pressure of gases could be accounted 
for by assuming their molecules to be moving uniformly in 
rectilinear paths. The same hypothesis was now seen to 
account for Avogadro’s law, that in equal volumes of dif¬ 
ferent kinds of gases exposed to the same pressure and 
temperature are contained equal numbers of molecules. 
Shortly after, it was found to account for the laws of diffu¬ 
sion and viscosity of gases, and for the numerical relation 
between these properties. Finally, Crookes’s radiometer 
furnished the last link in the strongest chain of evidence 
which supports any physical hypothesis. 

Such being the constitution of gases, liquids must clearly 
be bodies in which the molecules wander in curvilinear 
paths, while in solids they move in orbits or quasi-orbits. 
(See my definition solid II, 1, in the Century Dictionary .) 


240 


LOVE AND CHANCE 


We see that the resistance to compression and to inter¬ 
penetration between sensible bodies is, by one of the prime 
propositions of the molecular theory, due in large measure 
to the kinetical energy of the particles, which must be 
supposed to be quite remote from one another, on the aver¬ 
age, even in solids. This resistance is no doubt influenced 
by finite attractions and repulsions between the molecules. 
All the impenetrability of bodies which we can observe is, 
therefore, a limited impenetrability due to kinetic and 
positional energy. This being the case, we have no logical 
right to suppose that absolute impenetrability, or the ex¬ 
clusive occupancy of space, belongs to molecules or to 
atoms. It is an unwarranted hypothesis, not a vera causa . 3 
Unless we are to give up the theory of energy, finite posi¬ 
tional attractions and repulsions between molecules must 
be admitted. Absolute impenetrability would amount to 
an infinite repulsion at a certain distance. No analogy of 
known phenomena exists to excuse such a wanton violation 
of the principle of continuity as such a hypothesis is. In 
short, we are logically bound to adopt the Boscovichian idea 
that an atom is simply a distribution of component potential 
energy throughout space (this distribution being absolutely 
rigid), combined with inertia. The potential energy be¬ 
longs to two molecules, and is to be conceived as different 
between molecules A and B from what it is between mole¬ 
cules A and C. The distribution of energy is not neces¬ 
sarily spherical. Nay, a molecule may conceivably have 
more than one center; it may even have a central curve, 

3 By a vera causa, in the logic of science, is meant a state of things 
known to exist in some cases and supposed to exist in other cases, because 
it would account for observed phenomena. 


MAN’S GLASSY ESSENCE 


241 


returning into itself. But I do not think there are any 
observed facts pointing to such multiple or linear centers. 
On the other hand, many facts relating to crystals, espe¬ 
cially those observed by Voigt, 4 go to show that the distribu¬ 
tion of energy is harmonical but not concentric. We can 
easily calculate the forces which such atoms must exert 
upon one another by considering 5 that they are equivalent 
to aggregations of pairs of electrically positive and negative 
points infinitely near to one another. About such an atom 
there would be regions of positive and of negative potential, 
and the number and distribution of such regions would 
determine the valency of the atom, a number which it is 
easy to see would in many cases be somewhat indeterminate. 
I must not dwell further upon this hypothesis, at present. 
In another paper, its consequences will be further con¬ 
sidered. 

I cannot assume that the students of philosophy who 
read this magazine are thoroughly versed in modern molec¬ 
ular physics, and, therefore, it is proper to mention that 
the governing principle in this branch of science is Clausius’s 
law of the virial. I will first state the law, and then explain 
the peculiar terms of the statement. This statement is that 
the total kinetic energy of the particles of a system in sta¬ 
tionary motion is equal to the total virial. By a system 
is here meant a number of particles acting upon one an¬ 
other. 6 Stationary motion is a quasi-orbital motion among 

4 Wiedemann, Annalen, 1887-1889. 

5 See Maxwell on Spherical Harmonics, in his Electricity and 
Magnetism. 

6 The word system has three peculiar meanings in mathematics. ( 4 .) 
It means an orderly exposition of the truths of astronomy, and hence 


242 


LOVE AND CHANCE 


a system of particles so that none of them are removed to 
indefinitely great distances nor acquire indefinitely great 
velocities. The kinetic energy of a particle is the work 
which would be required to bring it to rest ; independently 
of any forces which may be acting upon it. The virial of 
a pair of particles is half the work which the force which 
actually operates between them would do if, being inde¬ 
pendent of the distance, it were to bring them together. 
The equation of the virial is 

§2wz> 2 = §22i?r. 

Here m is the mass of a particle, v its velocity, R is the 
attraction between two particles, and r is the distance be¬ 
tween them. The sign 2 on the left hand side signifies 
that the values of mv~ are to be summed for all the par¬ 
ticles, and 22 on the right hand side signifies that the 
values of Rr are to be summed for all the pairs of particles. 
If there is an external pressure P (as from the atmosphere) 
upon the system, and the volume of vacant space within 
the boundary of that pressure is V, then the virial must be 
understood as including J PV, so that the equation is 

§:w = I PV + §22 Rr. 

There is strong (if not demonstrative) reason for thinking 
that the temperature of any body above the absolute zero 
(~ 2 73° C.), is proportional to the average kinetic energy 

a theory of the motions of the stars; as the Ptolemaic system, the Coper- 
mean system. This is much like the sense in which we speak of the 
Calvinistic system of theology, the Kantian system of philosophy, etc. 
(B.) It means the aggregate of the planets considered as all moving in 
somewhat the same way, as the solar system; and hence any aggregate 
of particles moving under mutual forces. (C.) It means a number of 
forces acting simultaneously upon a number of particles. 


MAN’S GLASSY ESSENCE 


243 


of its molecules, or say a 6 , where a is a constant and 9 is 
the absolute temperature. Hence, we may write the equa¬ 
tion 


ad = bnv 2 = fPF + 


where the heavy lines above the different expressions signify 
that the average values for single molecules are to be taken. 
In 1872, a student in the University of Leyden, Van der 
Waals, propounded in his thesis for the doctorate a special¬ 
ization of the equation of the virial which has since attracted 
great attention. Namely, he writes it 



The quantity b is the volume of a molecule, which he sup¬ 
poses to be an impenetrable body, and all the virtue of the 
equation lies in this term which makes the equation a cubic 
in V , which is required to account for the shape of certain 
isothermal curves. 7 But if the idea of an impenetrable 
atom is illogical, that of an impenetrable molecule is almost 
absurd. For the kinetical theory of matter teaches us that 
a molecule is like a solar system or star-cluster in miniature. 
Unless we suppose that in all heating of gases and vapors 
internal work is performed upon the molecules, implying 
that their atoms are at considerable distances, the whole 
kinetical theory of gases falls to the ground. As for the 
term added to P, there is no more than a partial and roughly 
approximative justification for it. Namely, let us imagine 

7 But, in fact, an inspection of these curves is sufficient to show that 
they are of a higher degree than the third. For they have the line F=o, 
or some line V a constant for an asymptote, while for small values of 
P t the values of d 2 p/(dV ) 2 are positive. 


244 


LOVE AND CHANCE 


two spheres described round a particle as their center, 
the radius of the larger being so great as to include all the 
particles whose action upon the center is sensible, while 
the radius of the smaller is so large that a good many mole¬ 
cules are included within it. The possibility of describing 
such a sphere as the outer one implies that the attraction 
of the particles varies at some distances inversely as some 
higher power of the distance than the cube, or, to speak 
more clearly, that the attraction multiplied by the cube 
of the distance diminishes as the distance increases; for the 
number of particles at a given distance from any one par¬ 
ticle is proportionate to the square of that distance and 
each of these gives a term of the virial which is the product 
of the attraction into the distance. Consequently, unless 
the attraction multiplied by the cube of the distance di¬ 
minished so rapidly with the distance as soon to become in¬ 
sensible, no such outer sphere as is supposed could be de¬ 
scribed. However, ordinary experience shows that such a 
sphere is possible; and consequently there must be distances 
at which the attraction does thus rapidly diminish as the 
distance increases. The two spheres, then, being so drawn, 
consider the virial of the central particle due to the particles 
between them. Let the density of the substance be in¬ 
creased, say, N times. Then, for every turn, Rr, of the 
virial before the condensation, there will be N terms of the 
same magnitude after the condensation. Hence, the virial 
of each particle will be proportional to the density, and the 
equation of the virial becomes 


oB = PV + =■ 
V 


MAN’S GLASSY ESSENCE 


245 


This omits the virial within the inner sphere, the radius of 
which is so taken that within that distance the number of 
particles is not proportional to the number in a large sphere. 
For Van der Waals this radius is the diameter of his hard 
molecules, which assumption gives his equation. But it is 
plain that the attraction between the molecules must to 
a certain extent modify their distribution, unless some pe¬ 
culiar conditions are fulfilled. The equation of Van der 
Waals can be approximately true, therefore, only for a gas. 
In a solid or liquid condition, in which the removal of a 
small amount of pressure has little effect on the volume, 
and where consequently the virial must be much greater 
than PV, the virial must increase with the volume. For 
suppose we had a substance in a critical condition in which 
an increase of the volume would diminish the virial more 
than it would increase | PV. If we were forcibly to diminish 
the volume of such a substance, when the temperature be¬ 
came equalized, the pressure which it could withstand would 
be less than before, and it would be still further condensed, 
and this would go on indefinitely until a condition were 
reached in which an increase of volume would increase 
|PV more than it would decrease the virial. In the case 
of solids, at least, P may be zero; so that the state reached 
would be one in which the virial increases with the volume, 
or the attraction between the particles does not increase so 
fast with a diminution of their distance as it would if the 
attraction were inversely as the distance. 

Almost contemporaneously with Van der Waals’s paper, 
another remarkable thesis for the doctorate was presented 
at Paris by Amagat. It related to the elasticity and ex- 


246 


LOVE AND CHANCE 


pansion of gases, and to this subject the superb experi¬ 
menter, its author, has devoted his whole subsequent life. 
Especially interesting are his observations of the volumes of 
ethylene and of carbonic acid at temperatures from 20° to 
ioo° and at pressures ranging from an ounce to 5000 pounds 
to the square inch. As soon as Amagat had obtained these 
results, he remarked that the “ coefficient of expansion at 
constant volume,” as it is absurdly called, that is, the rate 
of variation of the pressure with the temperature, was very 
nearly constant for each volume. This accords with the 
equation of the virial, which gives 

dp _ __ dXRr 

dO ~ V d-d 

Now, the virial must be nearly independent of the tempera¬ 
ture, and, therefore, the last term almost disappears. The 
virial would not be quite independent of the temperature, 
because if the temperature (i.e., the square of the velocity 
of the molecules) is lowered, and the pressure correspond¬ 
ingly lowered, so as to make the volume the same, the at¬ 
tractions of the molecules will have more time to produce 
their effects, and consequently, the pairs of molecules the 
closest together will be held together longer and closer; 
so that the virial will generally be increased by a decrease 
of temperature. Now, Amagat’s experiments do show an 
excessively minute effect of this sort, at least, when the 
volumes are not too small. However, the observations are 
well enough satisfied by assuming the “ coefficient of ex¬ 
pansion at constant volume ” to consist wholly of the first 
term, a/V. Thus, Amagat’s experiments enable us to de- 



MAN’S GLASSY ESSENCE 


247 


termine the values of a and thence to calculate the virial; 
and this we find varies for carbonic acid gas nearly inversely 
to F 0,9 . There is, thus, a rough approximation to satisfy¬ 
ing Van der Waals’s equation. But the most interesting 
result of Amagat’s experiments, for our purpose at any 
rate, is that the quantity a, though nearly constant for any 
one volume, differs considerably with the volume, nearly 
doubling when the volume is reduced fivefold. This can 
only indicate that the mean kinetic energy of a given mass 
of the gas for a given temperature is greater the more the 
gas is compressed. But the laws of mechanics appear to 
enjoin that the mean kinetic energy of a moving particle 
shall be constant at any given temperature. The only 
escape from contradiction, then, is to suppose that the 
mean mass of a moving particle diminishes upon the con¬ 
densation of the gas. In other words, many of the mole¬ 
cules are dissociated, or broken up into atoms or sub¬ 
molecules. The idea that dissociation should be favored 
by diminishing the volume will be pronounced by physicists, 
at first blush, as contrary to all our experience. But it 
must be remembered that the circumstances we are speaking 
of, that of a gas under fifty or more atmospheres pressure, 
are also unusual. That the “ coefficient of expansion under 
constant volume ” when multiplied by the volumes should 
increase with a decrement of the volume is also quite con¬ 
trary to ordinary experience; yet it undoubtedly takes place 
in all gases under great pressure. Again, the doctrine of 
Arrhenius 8 is now generally accepted, that the molecular 

8 Anticipated by Clausius as long ago as 1857; and by Williamson in 
1851. 


248 


LOVE AND CHANCE 


conductivity of an electrolyte is proportional to the dis¬ 
sociation of ions. Now the molecular conductivity of a 
fused electrolyte is usually superior to that of a solution. 
Here is a case, then, in which diminution of volume is ac¬ 
companied by increased dissociation. 

The truth is that several different kinds of dissociation 
have to be distinguished. In the first place, there is the 
dissociation of a chemical molecule to form chemical mole¬ 
cules under the regular action of chemical laws. This may 
be a double decomposition, as when iodhydric acid is dis¬ 
sociated, according to the formula 

HI + HI = HE + II; 

or, it may be a simple decomposition, as when pentachloride 
of phosphorus is dissociated according to the formula 

PCk = PCI 3 + CICl. 

All these dissociations require, according to the laws of 
thermo-chemistry, an elevated temperature. In the second 
place, there is the dissociation of a physically polymerous 
molecule, that is, of several chemical molecules joined by 
physical attractions. This I am inclined to suppose is a 
common concomitant of the heating of solids and liquids; 
for in these bodies there is no increase of compressibility 
with the temperature at all comparable with the increase 
of the expansibility. But, in the third place, there is the 
dissociation with which we are now concerned, which must 
be supposed to be a throwing off of unsaturated sub-mole¬ 
cules or atoms from the molecule. The molecule may, as 
I have said, be roughly likened to a solar system. As such, 


MAN’S GLASSY ESSENCE 


249 


molecules are able to produce perturbations of one another’s 
internal motions; and in this way a planet, i.e., a sub-mole¬ 
cule, will occasionally get thrown off and wander about by 
itself, till it finds another unsaturated sub-molecule with 
which it can unite. Such dissociation by perturbation will 
naturally be favored by the proximity of the molecules to 
one another. 

Let us now pass to the consideration of that special sub¬ 
stance, or rather class of substances, whose properties form 
the chief subject of botany and of zoology, as truly as those 
of the silicates form the chief subject of mineralogy: I mean 
the life-slimes, or protoplasm. Let us begin by cataloguing 
the general characters of these slimes. They one and all 
exist in two states of aggregation, a solid or nearly solid 
state and a liquid or nearly liquid state; but they do not 
pass from the former to the latter by ordinary fusion. They 
are readily decomposed by heat, especially in the liquid 
state; nor will they bear any considerable degree of cold. 
All their vital actions take place at temperatures very little 
below the point of decomposition. This extreme instability 
is one of numerous facts which demonstrate the chemical 
complexity of protoplasm. Every chemist will agree that 
they are far more complicated than the albumens. Now, 
albumen is estimated to contain in each molecule about a 
thousand atoms; so that it is natural to suppose that the 
protoplasms contain several thousands. We know that 
while they are chiefly composed of oxygen, hydrogen, car¬ 
bon, and nitrogen, a large number of other elements enter 
into living bodies in small proportions; and it is likely that 
most of these enter into the composition of protoplasms. 


250 


LOVE AND CHANCE 


Now, since the numbers of chemical varieties increase at 
an enormous rate with the number of atoms per molecule, 
so that there are certainly hundreds of thousands of sub¬ 
stances whose molecules contain twenty atoms or fewer, 
we may well suppose that the number of protoplasmic 
substances runs into the billions or trillions. Professor 
Cayley has given a mathematical theory of “ trees,” with 
a view of throwing a light upon such questions; and in that 
light the estimate of trillions (in the English sense) seems 
immoderately moderate. It is true that an opinion has 
been emitted, and defended among biologists, that there is 
but one kind of protoplasm; but the observations of biolo¬ 
gists, themselves, have almost exploded that hypothesis, 
which from a chemical standpoint appears utterly incredible. 
The anticipation of the chemist would decidedly be that 
enough different chemical substances having protoplasmic 
characters might be formed to account, not only for the 
differences between nerve-slime and muscle-slime, between 
whale-slime and lion-slime, but also for those minuter per¬ 
vasive variations which characterize different breeds and 
single individuals. 

Protoplasm, when quiescent, is, broadly speaking, solid; 
but when it is disturbed in an appropriate way, or some¬ 
times even spontaneously without external disturbance, it 
becomes, broadly speaking, liquid. A moner in this state 
is seen under the microscope to have streams within its 
matter; a slime-mould slowly flows by force of gravity. 
The liquefaction starts from the point of disturbance and 
spreads through the mass. This spreading, however, is not 
uniform in all directions; on the contrary, it takes at one 


MAN’S GLASSY ESSENCE 


251 


time one course, at another another, through the homo¬ 
geneous mass, in a manner that seems a little mysterious. 
The cause of disturbance being removed, these motions 
gradually (with higher kinds of protoplasm, quickly) cease, 
and the slime returns to its solid condition. 

The liquefaction of protoplasm is accompanied by a me¬ 
chanical phenomenon. Namely, some kinds exhibit a ten¬ 
dency to draw themselves up into a globular form. This 
happens particularly with the contents of muscle-cells. The 
prevalent opinion, founded on some of the most exquisite 
experimental investigations that the history of science can 
show, is undoubtedly that the contraction of muscle-cells 
is due to osmotic pressure; and it must be allowed that 
that is a factor in producing the effect. But it does not 
seem to me that it satisfactorily accounts even for the phe¬ 
nomena of muscular contraction; and besides, even naked 
slimes often draw up in the same way. In this case, we 
seem to recognize an increase of the surface-tension. In 
some cases, too, the reverse action takes place, extraordinary 
pseudopodia being put forth, as if the surface-tension were 
diminished in spots. Indeed, such a slime always has a sort 
of skin, due no doubt to surface-tension, and this seems to 
give way at the point where a pseudopodium is put forth. 

Long-continued or frequently repeated liquefaction of 
the protoplasm results in an obstinate retention of the solid 
state, which we call fatigue. On the other hand, repose 
in this state, if not too much prolonged, restores the lique- 
fiability. These are both important functions. 

The life-slimes have, further, the peculiar property of 
growing. Crystals also grow; their growth, however, con- 


252 


LOVE AND CHANCE 


sists merely in attracting matter like their own from the 
circumambient fluid. To suppose the growth of protoplasm 
of the same nature, would be to suppose this substance to 
be spontaneously generated in copious supplies wherever 
food is in solution. Certainly, it must be granted that 
protoplasm is but a chemical substance, and that there is 
no reason why it should not be formed synthetically like 
any other chemical substance. Indeed, Clifford has clearly 
shown that we have overwhelming evidence that it is so 
formed. But to say that such formation is as regular and 
frequent as the assimilation of food is quite another matter. 
It is more consonant with the facts of observation to sup¬ 
pose that assimilated protoplasm is formed at the instant of 
assimilation, under the influence of the protoplasm already 
present. For each slime in its growth preserves its distinc¬ 
tive characters with wonderful truth, nerve-slime growing 
nerve-slime and muscle-slime muscle-slime, lion-slime grow¬ 
ing lion-slime, and all the varieties of breeds and even in¬ 
dividual characters being preserved in the growth. Now 
it is too much to suppose there are billions of different kinds 
of protoplasm floating about wherever there is food. 

The frequent liquefaction of protoplasm increases its 
power of assimilating food; so much so, indeed, that it is 
questionable whether in the solid form it possesses this 
power. 

The life-slime wastes as well as grows; and this too takes 
place chiefly if not exclusively in its liquid phases. 

Closely connected with growth is reproduction; and 
though in higher forms this is a specialized function, it is 
universally true that wherever there is protoplasm, there is, 


MAN’S GLASSY ESSENCE 


253 


will be, or has been a power of reproducing that same kind 
of protoplasm in a separated organism. Reproduction 
seems to involve the union of two sexes; though it is not 
demonstrable that this is always requisite. 

Another physical property of protoplasm is that of taking 
habits. The course which the spread of liquefaction has 
taken in the past is rendered thereby more likely to be taken 
in the future; although there is no absolute certainly that 
the same path will be followed again. 

Very extraordinary, certainly, are all these properties of 
protoplasm; as extraordinary as indubitable. But the one 
which has next to be mentioned, while equally undeniable, 
is infinitely more wonderful. It is that protoplasm feels. 
We have no direct evidence that this is true of protoplasm 
universally, and certainly some kinds feel far more than 
others. But there is a fair analogical inference that all 
protoplasm feels. It not only feels but exercises all the 
functions of mind. 

Such are the properties of protoplasm. The problem is 
to find a hypothesis of the molecular constitution of this 
compound which will account for these properties, one 
and all. 

Some of them are obvious results of the excessively com¬ 
plicated constitution of the protoplasm molecule. All very 
complicated substances are unstable; and plainly a mole¬ 
cule of several thousand atoms may be separated in many 
ways into two parts in each of which the polar chemical 
forces are very nearly saturated. In the solid protoplasm, 
as in other solids, the molecules must be supposed to be 
moving as it were in orbits, or, at least, so as not to wander 


254 


LOVE AND CHANCE 


indefinitely. But this solid cannot be melted, for the same 
reason that starch cannot be melted; because an amount of 
heat insufficient to make the entire molecules wander is 
sufficient to break them up completely and cause them to 
form new and simpler molecules. But when one of the 
molecules is disturbed, even if it be not quite thrown out 
of its orbit at first, sub-molecules of perhaps several hun¬ 
dred atoms each are thrown off from it. These will soon 
acquire the same mean kinetic energy as the others, and, 
therefore, velocities several times as great. They will 
naturally begin to wander, and in wandering will perturb 
a great many other molecules and cause them in their turn 
to behave like the one originally deranged. So many mole¬ 
cules will thus be broken up, that even those that are in¬ 
tact will no longer be restrained within orbits, but will wan¬ 
der about freely. This is the usual condition of a liquid, 
as modern chemists understand it; for in all electrolytic 
liquids there is considerable dissociation. 

But this process necessarily chills the substance, not 
merely on account of the heat of chemical combination, 
but still more because the number of separate particles 
being greatly increased, the mean kinetic energy must be 
less. The substance being a bad conductor, this heat is 
not at once restored. Now the particles moving more 

slowly, the attractions between them have time to take 

\ 

effect, and they approach the condition of equilibrium. 
But their dynamic equilibrium is found in the restoration 
of the solid condition, which, therefore, takes place, if the 
disturbance is not kept up. 

When a body is in the solid condition, most of its mole- 


MAN’S GLASSY ESSENCE 


255 


cules must be moving at the same rate, or, at least, at certain 
regular sets of rates; otherwise the orbital motion would not 
be preserved. The distances of neighboring molecules 
must always be kept between a certain maximum and a 
certain minimum value. But if, without absorption of 
heat, the body be thrown into a liquid condition, the dis¬ 
tances of neighboring molecules will be far more unequally 
distributed, and an effect upon the virial will result. The 
chilling of protoplasm upon its liquefaction must also be 
taken into account. The ordinary effect will no doubt be 
to increase the cohesion and with that the surface-tension, 
so that the mass will tend to draw itself up. But in special 
cases, the virial will be increased so much that the surface- 
tension will be diminished at points where the temperature 
is first restored. In that case, the outer film will give way 
and the tension at other places will aid in causing the gen¬ 
eral fluid to be poured out at those points, forming 
pseudopodia. 

When the protoplasm is in a liquid state, and then only, 
a solution of food is able to penetrate its mass by diffusion. 
The protoplasm is then considerably dissociated; and so is 
the food, like all dissolved matter. If then the separated 
and unsaturated sub-molecules of the food happen to be 
of the same chemical species as sub-molecules of the proto¬ 
plasm, they may unite with other sub-molecules of the 
protoplasm to form new molecules, in such a fashion that 
when the solid state is resumed, there may be more mole¬ 
cules of protoplasm than there were at the beginning. It 
is like the jackknife whose blade and handle, after having 
been severally lost and replaced, were found and put to¬ 
gether to make a new knife. 


256 


LOVE AND CHANCE 


We have seen that protoplasm is chilled by liquefaction, 
and that this brings it back to the solid state, when the heat 
is recovered. This series of operations must be very rapid 
in the case of nerve-slime and even of muscle-slime, and 
may account for the unsteady or vibratory character of 
their action. Of course, if assimilation takes place, the 
heat of combination, which is probably trifling, is gained. 
On the other hand, if work is done, whether by nerve or by 
muscle, loss of energy must take place. In the case of 
the muscle, the mode by which the instantaneous part of 
the fatigue is brought about is easily traced out. If when 
the muscle contracts it be under stress, it will contract less 
than it otherwise would do, and there will be a loss of heat. 
It is like an engine which should work by dissolving salt 
in water and using the contraction during the solution to 
lift a weight, the salt being recovered afterwards by dis¬ 
tillation. But the major part of fatigue has nothing to do 
with the correlation of forces. A man must labor hard to 
do in a quarter of an hour the work which draws from him 
enough heat to cool his body by a single degree. Mean¬ 
time, he will be getting heated, he will be pouring out extra 
products of combustion, perspiration, etc., and he will be 
driving the blood at an accelerated rate through minute 
tubes at great expense. Yet all this will have little to do 
with his fatigue. He may sit quietly at his table writing, 
doing practically no physical work at all, and yet in a few 
hours be terribly fagged. This seems to be owing to the 
deranged sub-molecules of the nerve-slime not having had 
time to settle back into their proper combinations. When 
such sub-molecules are thrown out, as they must be from 
time to time, there is so much waste of material. 


MAN’S GLASSY ESSENCE 


257 


In order that a sub-molecule of food may be thoroughly 
and firmly assimilated into a broken molecule of proto¬ 
plasm, it is necessary not only that it should have precisely 
the right chemical composition, but also that it should be 
at precisely the right spot at the right time and should be 
moving in precisely the right direction with precisely the 
right velocity. If all these conditions are not fulfilled, it 
will be more loosely retained than the other parts of the 
molecule; and every time it comes round into the situation 
in which it was drawn in, relatively to the other parts of 
that molecule and to such others as were near enough to 
be factors in the action, it will be in special danger of being 
thrown out again. Thus, when a partial liquefaction of 
the protoplasm takes place many times to about the same 
extent, it will, each time, be pretty nearly the same mole¬ 
cules that were last drawn in that are now thrown out. 
They will be thrown out, too, in about the same way, as to 
position, direction of motion, and velocity, in which they 
were drawn in; and this will be in about the same course 
that the ones last before them were thrown out. Not ex¬ 
actly, however; for the very cause of their being thrown 
off so easily is their not having fulfilled precisely the con¬ 
ditions of stable retention. Thus, the law of habit is ac¬ 
counted for, and with it its peculiar characteristic of not 
acting with exactitude. 

It seems to me that this explanation of habit, aside from 
the question of its truth or falsity, has a certain value as an 
addition to our little store of mechanical examples of actions 
analogous to habit. All the others, so far as I know, are 
either statical or else involve forces which, taking only the 


258 


LOVE AND CHANCE 


sensible motions into account, violate the law of energy. 
It is so with the stream that wears its own bed. Here, the 
sand is carried to its most stable situation and left there. 
The law of energy forbids this; for when anything reaches 
a position of stable equilibrium, its momentum will be at 
a maximum, so that it can according to this law only be 
left at rest in an unstable situation. In all the statical 
illustrations, too, things are brought into certain states and 
left there. A garment receives folds and keeps them; that 
is, its limit of elasticity is exceeded. This failure to spring 
back is again an apparent violation of the law of energy; 
for the substance will not only not spring back of itself 
(which might be due to an unstable equilibrium being 
reached) but will not even do so when an impulse that way 
is applied to it. Accordingly, Professor James says, “ the 
phenomena of habit . . . are due to the plasticity of the 
. . . materials.” Now, plasticity of materials means the 
having of a low limit of elasticity. (See the Century 
Dictionary, under solid.) But the hypothetical constitu¬ 
tion of protoplasm here proposed involves no forces but 
attractions and repulsions strictly following the law of 
energy. The action here, that is, the throwing of an atom 
out of its orbit in a molecule, and the entering of a new 
atom into nearly, but not quite the same orbit, is somewhat 
similar to the molecular actions which may be supposed 
to take place in a solid strained beyond its limit of elasticity. 
Namely, in that case certain molecules must be thrown out 
of their orbits, to settle down again shortly after into new 
orbits. In short, the plastic solid resembles protoplasm in 
being partially and temporarily liquefied by a slight me- 


MAN’S GLASSY ESSENCE 


259 


chanical force. But the taking of a set by a solid body 
has but a moderate resemblance to the taking of a habit, 
inasmuch as the characteristic feature of the latter, its 
inexactitude and want of complete determinacy, is not so 
marked in the former, if it can be said to be present there, 
at all. 

The t\*uth is that though the molecular explanation of 
habit is pretty vague on the mathematical side, there can 
be no doubt that systems of atoms having polar forces 
would act substantially in that manner, and the explanation 
is even too satisfactory to suit the convenience of an advo¬ 
cate of tychism. For it may fairly be urged that since the 
phenomena of habit may thus result from a purely me¬ 
chanical arrangement, it is unnecessary to suppose that 
habit-taking is a primordial principle of the universe. But 
one fact remains unexplained mechanically, which concerns 
not only the facts of habit, but all cases of actions appar¬ 
ently violating the law of energy; it is that all these phe¬ 
nomena depend upon aggregations of trillions of molecules 
in one and the same condition and neighborhood; and it is 
by no means clear how they could have all been brought 
and left in the same place and state by any conservative 
forces. But let the mechanical explanation be as perfect 
as it may, the state of things which it supposes presents 
evidence of a primordial habit-taking tendency. For it 
shows us like things acting in like ways because they are 
alike. Now, those who insist on the doctrine of necessity 
will for the most part insist that the physical world is en¬ 
tirely individual. Yet law involves an element of gener¬ 
ality. Now to say that generality is primordial, but gen- 


26 o 


LOVE AND CHANCE 


eralization not, is like saying that diversity is primordial 
but diversification not. It turns logic upside down. At 
any rate, it is clear that nothing but a principle of habit, 
itself due to the growth by habit of an infinitesimal chance 
tendency toward habit-taking, is the only bridge that can 
span the chasm between the chance-medley of chaos and 
the cosmos of order and law. 

I shall not attempt a molecular explanation of the phe¬ 
nomena of reproduction, because that would require a sub¬ 
sidiary hypothesis, and carry me away from my main 
object. Such phenomena, universally diffused though they 
be, appear to depend upon special conditions; and we do 
not find that all protoplasm has reproductive powers. 

But what is to be said of the property of feeling? If 
consciousness belongs to all protoplasm, by what mechani¬ 
cal constitution is this to be accounted for? The slime 
is nothing but a chemical compound. There is no inherent 
impossibility in its being formed synthetically in the labora¬ 
tory, out of its chemical elements; and if it were so made, 
it would present all the characters of natural protoplasm. 
No doubt, then, it would feel. To hesitate to admit this 
would be puerile and ultra-puerile. By what element of 
the molecular arrangement, then, would that feeling be 
caused? This question cannot be evaded or pooh-poohed. 
Protoplasm certainly does feel; and unless we are to accept 
a weak dualism, the property must be shown to arise from 
some peculiarity of the mechanical system. Yet the at¬ 
tempt to deduce it from the three laws of mechanics, ap¬ 
plied to never so ingenious a mechanical contrivance, would 
obviously be futile. It can never be explained, unless we 


MAN’S GLASSY ESSENCE 


261 


admit that physical events are but degraded or undeveloped 
forms of psychical events. But once grant that the phe¬ 
nomena of matter are but the result of the sensibly com¬ 
plete sway of habits upon mind, and it only remains to 
explain why in the protoplasm these habits are to some 
slight extent broken up, so that according to the law of 
mind, in that special clause of it sometimes called the prin¬ 
ciple of accommodation , 9 feeling becomes intensified. Now 
the manner in which habits generally get broken up is this. 
Reactions usually terminate in the removal of a stimulus; 
for the excitation continues as long as the stimulus is pres¬ 
ent. Accordingly, habits are general ways of behavior 
which are associated with the removal of stimuli. But 
when the expected removal of the stimulus fails to occur, 
the excitation continues and increases, and non-habitual 
reactions take place; and these tend to weaken the habit. 
If, then, we suppose that matter never does obey its ideal 
laws with absolute precision, but that there are almost in¬ 
sensible fortuitous departures from regularity, these will 
produce, in general, equally minute effects. But proto¬ 
plasm is in an excessively unstable condition; and it is the 
characteristic of unstable equilibrium, that near that point 
excessively minute causes may produce startlingly large 
effects. Here, then, the usual departures from regularity 
will be followed by others that are very great; and the large 
fortuitous departures from law so produced, will tend still 
further to break up the laws, supposing that these are of 


9 “ Physiologically, . . . accommodation means the breaking up of a 
habit. . . . Psychologically, it means reviving consciousness.” Baldwin, 
Psychology, Part III, ch. i., § 5. 


262 


LOVE AND CHANCE 


the nature of habits. Now, this breaking up of habit and 
renewed fortuitous spontaneity will, according to the law 
of mind, be accompanied by an intensification of feeling. 
The nerve-protoplasm is, without doubt, in the most un¬ 
stable condition of any kind of matter; and consequently, 
there the resulting feeling is the most manifest. 

Thus we see that the idealist has no need to dread a 
mechanical theory of life. On the contrary, such a theory, 
fully developed, is bound to call in a tychistic idealism as 
its indispensable adjunct. Wherever chance-spontaneity 
is found, there, in the same proportion, feeling exists. In 
fact, chance is but the outward aspect of that which within 
itself is feeling. I long ago showed that real existence, or 
thing-ness, consists in regularities. So, that primeval chaos 
in which there was no regularity was mere nothing, from 
a physical aspect. Yet it was not a blank zero; for there 
was an intensity of consciousness there in comparison with 
which all that we ever feel is but as the struggling of a 
molecule or two to throw off a little of the force of law to 
an endless and innumerable diversity of chance utterly un¬ 
limited. 

But after some atoms of the protoplasm have thus become 
partially emancipated from law, what happens next to them? 
To understand this, we have to remember that no mental 
tendency is so easily strengthened by the action of habit 
as is the tendency to take habits. Now, in the higher kinds 
of protoplasm, especially, the atoms in question have not 
only long belonged to one molecule or another of the par¬ 
ticular mass of slime of which they are parts; but before 
that, they were constituents of food of a protoplasmic con- 


MAN’S GLASSY ESSENCE 


263 

stitution. During all this time, they have been liable to 
lose habits and to recover them again; so that now, when 
the stimulus is removed, and the foregone habits tend to 
reassert themselves, they do so in the case of such atoms 
with great promptness. Indeed, the return is so prompt 
that there is nothing but the feeling to show conclusively 
that the bonds of law have ever been relaxed. 

In short, diversification is the vestige of chance-spon¬ 
taneity; and wherever diversity is increasing, there chance 
must be operative. On the other hand, wherever uniformity 
is increasing, habit must be operative. But wherever ac¬ 
tions take place under an established uniformity, there so 
much feeling as there may be takes the mode of a sense of 
reaction. That is the manner in which I am led to define 
the relation between the fundamental elements of conscious¬ 
ness and their physical equivalents. 

It remains to consider the physical relations of general 
ideas. It may be well here to reflect that if matter has no 
existence except as a specialization of mind, it follows that 
whatever affects matter according to regular laws is itself 
matter. But all mind is directly or indirectly connected 
with all matter, and acts in a more or less regular way; 
so that all mind more or less partakes of the nature of 
matter. Hence, it would be a mistake to conceive of the 
psychical and the physical aspects of matter as two aspects 
absolutely distinct. Viewing a thing from the outside, con¬ 
sidering its relations of action and reaction with other 
things, it appears as matter. Viewing it from the inside, 
looking at its immediate character as feeling, it appears as 
consciousness. These two views are combined when we 


264 


LOVE AND CHANCE 


remember that mechanical laws are nothing but acquired 
habits, like all the regularities of mind, including the ten¬ 
dency to take habits, itself; and that this action of habit 
is nothing but generalization, and generalization is nothing 
but the spreading of feelings. But the question is, how do 
general ideas appear in the molecular theory of protoplasm? 

The consciousness of a habit involves a general idea. In 
each action of that habit certain atoms get thrown out of 
their orbit, and replaced by others. Upon all the different 
occasions it is different atoms that are thrown off, but they 
are analogous from a physical point of view, and there is 
an inward sense of their being analogous. Every time 
one of the associated feelings recurs, there is a more or less 
vague sense that there are others, that it has a general 
character, and of about what this general character is. We 
ought not, I think, to hold that in protoplasm habit never 
acts in any other than the particular way suggested above. 
On the contrary, if habit be a primary property of mind, 
it must be equally so of matter, as a kind of mind. We 
can hardly refuse to admit that wherever chance motions 
have general characters, there is a tendency for this gener¬ 
ality to spread and to perfect itself. In that case, a general 
idea is a certain modification of consciousness which accom¬ 
panies any regularity or general relation between chance 
actions. 

The consciousness of a general idea has a certain “ unity 
of the ego,” in it, which is identical when it passes from 
one mind to another. It is, therefore, quite analogous to 
a person; and, indeed, a person is only a particular kind 
of general idea. Long age, in the Journal of Speculative 


MAN’S GLASSY ESSENCE 


26$ 

Philosophy (Vol. II, p. 156), I pointed out that a person 
is nothing but a symbol involving a general idea; but my 
views were, then, too nominalistic to enable me to see that 
every general idea has the unified living feeling of a person. 

All that is necessary, upon this theory, to the existence 
of a person is that the feelings out of which he is constructed 
should be in close enough connection to influence one an¬ 
other. Here we can draw a consequence which it may be 
possible to submit to experimental test. Namely, if this 
be the case, there should be something like personal con¬ 
sciousness in bodies of men who are in intimate and in¬ 
tensely sympathetic communion. It is true that when the 
generalization of feeling has been carried so far as to in¬ 
clude all within a person, a stopping-place, in a certain 
sense, has been attained; and further generalization will 
have a less lively character. But we must not think it will 
cease. Esprit de corps, national sentiment, sympathy, are 
no mere metaphors. None of us can fully realize what the 
minds of corporations are, any more than one of my brain- 
cells can know what the whole brain is thinking. But the 
law of mind clearly points to the existence of such per¬ 
sonalities, and there are many ordinary observations which, 
if they were critically examined and supplemented by special 
experiments, might, as first appearances promise, give evi¬ 
dence of the influence of such greater persons upon indi¬ 
viduals. It is often remarked that on one day half a dozen 
people, strangers to one another, will take it into their heads 
to do one and the same strange deed, whether it be a physi¬ 
cal experiment, a crime, or an act of virtue. When the 
thirty thousand young people of the society for Christian 


266 


LOVE AND CHANCE 


Endeavor were in New York, there seemed to me to be some 
mysterious diffusion of sweetness and light. If such a fact 
is capable of being made out anywhere, it should be in the 
church. The Christians have always been ready to risk 
their lives for the sake of having prayers in common, of 
getting together and praying simultaneously with great 
energy, and especially for their common body, for “ the 
whole state of Christ’s church militant here in earth,” as 
one of the missals has it. This practice they have been 
keeping up everywhere, weekly, for many centuries. 
Surely, a personality ought to have developed in that church, 
in that “ bride of Christ,” as they call it, or else there is a 
strange break in the action of mind, and I shall have to 
acknowledge my views are much mistaken. Would not the 
societies for psychical research be more likely to break 
through the clouds, in seeking evidences of such corporate 
personality, than in seeking evidences of telepathy, which, 
upon the same theory, should be a far weaker phenomenon? 


V. EVOLUTIONARY LOVE 1 


AT FIRST BLUSH. COUNTER-GOSPELS 

Philosophy, when just escaping from its golden pupa-skin, 
mythology, proclaimed the great evolutionary agency of the 
universe to be Love. Or, since this pirate-lingo, English, 
is poor in such-like words, let us say Eros, the exuberance- 
love. Afterwards, Empedocles set up passionate-love and 
hate as the two co-ordinate powers of the universe. In some 
passages, kindness is the word. But certainly, in any sense 
in which it has an opposite, to be senior partner of that 
opposite, is the highest position that love can attain. Never¬ 
theless, the ontological gospeller, in whose days those views 
were familiar topics, made the One Supreme Being, by 
whom all things have been made out of nothing, to be 
cherishing-love. What, then, can he say to hate? Never 
mind, at this time, what the scribe of the apocalypse, if he 
were John, stung at length by persecution into a rage unable 
to distinguish suggestions of evil from visions of heaven, 
and so become the Slanderer of God to men, may have 
dreamed. The question is rather what the sane John 
thought, or ought to have thought, in order to carry out 
his idea consistently. His statement that God is love seems 
aimed at that saying of Ecclesiastes that we cannot tell 
whether God bears us love or hatred. “ Nay,” says John, 
“we can tell, and very simply! We know and have 

1 The Monist, January, 1893. 

267 


268 


LOVE AND CHANCE 


ft 

trusted the love which God hath in us. God is love.” 
There is no logic in this, unless it means that God loves all 
men. In the preceding paragraph, he had said, “ God is 
light and in him is no darkness at all.” We are to under¬ 
stand, then, that as darkness is merely the defect of light, 
so hatred and evil are mere imperfect stages of ayairrj 
and ayaOov, love and loveliness. This concords with that 
utterance reported in John’s Gospel: “ God sent not the 
Son into the world to judge the world; but that the world 
should through him be saved. He that believeth on him is 
not judged: he that believeth not hath been judged al¬ 
ready. . . . And this is the judgment, that the light is 
come into the world, and that men loved darkness rather 
than the light.” That is to say, God visits no punishment 
on them; they punish themselves, by their natural affinity 
for the defective. Thus, the love that God is, is not a love 
of which hatred is the contrary; otherwise Satan would be 
a co-ordinate power; but it is a love which embraces hatred 
as an imperfect stage of it, an Anteros — yea, even needs 
hatred and hatefulness as its object. For self-love is no 
love; so if God’s self is love, that which he loves must be 
defect of love; just as a luminary can light up only that 
which otherwise would be dark. Henry James, the Sweden- 
borgian, says: “It is no doubt very tolerable finite or 
creaturely love to love one’s own in another, to love another 
for his conformity to one’s self: but nothing can be in 
more flagrant contrast with the creative Love, all whose 
tenderness ex vi termini must be reserved only for what 
intrinsically is most bitterly hostile and negative to itself.” 
This is from Substance and Shadow: an Essay on the 


EVOLUTIONARY LOVE 


269 


Physics of Creation. It is a pity he had not filled his pages 
with things like this, as he was able easily to do, instead of 
scolding at his reader and at people generally, until the 
physics of creation was well-nigh forgot. I must deduct, 
however, from what I just wrote: obviously no genius could 
make his every sentence as sublime as one which discloses 
for the problem of evil its everlasting solution. 

The movement of love is circular, at one and the same 
impulse projecting creations into independency and draw¬ 
ing them into harmony. This seems complicated when 
stated so; but it is fully summed up in the simple formula 
we call the Golden Rule. This does not, of course, say, 
Do everything possible to gratify the egoistic impulses of 
others, but it says, Sacrifice your own perfection to the 
perfectionment of your neighbor. Nor must it for a mo¬ 
ment be confounded with the Benthamite, or Helvetian, or 
Beccarian motto, Act for the greatest good of the greatest 
number. Love is not directed to abstractions but to per¬ 
sons; not to persons we do not know, nor to numbers of 
people, but to our own dear ones, our family and neighbors. 
“ Our neighbor,” we remember, is one whom we live near, 
not locally perhaps, but in life and feeling. 

Everybody can see that the statement of St. John is the 
formula of an evolutionary philosophy, which teaches that 
growth comes only from love, from — I will not say self- 
sacrijice, but from the ardent impulse to fulfil another’s 
highest impulse. Suppose, for example, that I have an idea 
that interests me. It is my creation. It is my creature; 
for as shown in last July’s Monist, it is a little person. I 
love it; and I will sink myself in perfecting it. It is not 


270 


LOVE AND CHANCE 


by dealing out cold justice to the circle of my ideas that 
I can make them grow, but by cherishing and tending them 
as I would the flowers in my garden. The philosophy we 
draw from John’s gospel is that this is the way mind de¬ 
velops ; and as for the cosmos, only so far as it yet is mind, 
and so has life, is it capable of further evolution. Love, 
recognizing germs of loveliness in the hateful, gradually 
warms it into life, and makes it lovely. That is the sort 
of evolution which every careful student of my essay The 
Law of Mindy must see that synechism calls for. 

The nineteenth century is now fast sinking into the grave, 
and we all begin to review its doings and to think what 
character it is destined to bear as compared with other 
centuries in the minds of future historians. It will be 
called, I guess, the Economical Century; for political 
economy has more direct relations with all the branches of 
its activity than has any other science. Well, political 
economy has its formula of redemption, too. It is this: 
Intelligence in the service of greed ensures the justest 
prices, the fairest contracts, the most enlightened conduct 
of all the dealings between men, and leads to the summutn 
bonum , food in plenty and perfect comfort. Food for 
whom? Why, for the greedy master of intelligence. I do 
not mean to say that this is one of the legitimate conclu¬ 
sions of political economy, the scientific character of which 
I fully acknowledge. But the study of doctrines, them¬ 
selves true, will often temporarily encourage generalizations 
extremely false, as the study of physics has encouraged 
necessitarianism. What I say, then, is that the great at¬ 
tention paid to economical questions during our century 


EVOLUTIONARY LOVE 


271 


has induced an exaggeration of the beneficial effects of 
greed and of the unfortunate results of sentiment, until 
there has resulted a philosophy which comes unwittingly 
to this, that greed is the great agent in the elevation of 
the human race and in the evolution of the universe. 

I open a handbook of political economy, — the most 
typical and middling one I have at hand, — and there find 
some remarks of which I will here make a brief analysis. 
I omit qualifications, sops thrown to Cerberus, phrases to 
placate Christian prejudice, trappings which serve to hide 
from author and reader alike the ugly nakedness of the 
greed-god. But I have surveyed my position. The author 
enumerates “ three motives to human action: 

The love of self; 

The love of a limited class having common interests and 
feelings with one’s self; 

The love of mankind at large.” 

Remark, at the outset, what obsequious title is bestowed 
on greed, — “the love of self.” Love! The second mo¬ 
tive is love. In place of “ a limited class ” put “ certain 
persons,” and you have a fair description. Taking “ class ” 
in the old-fashioned sense, a weak kind of love is described. 
In the sequel, there seems to be some haziness as to the 
delimitation of this motive. By the love of mankind at 
large, the author does not mean that deep, subconscious 
passion that is properly so called; but merely public-spirit, 
perhaps little more than a fidget about pushing ideas. The 
author proceeds to a comparative estimate of the worth of 
these motives. Greed, says he, but using, of course, an¬ 
other word, “ is not so great an evil as is commonly sup- 


LOVE AND CHANCE 


272 

posed. . . . Every man can promote his own interests a 
great deal more effectively than he can promote any one 
else’s, or than any one else can promote his.” Besides, as 
he remarks on another page, the more miserly a man is, 
the more good he does. The second motive “ is the most 
dangerous one to which society is exposed.” Love is all 
very pretty: “ no higher or purer source of human happi¬ 
ness exists.” (Ahem!) But it is a “source of enduring 
injury,” and, in short, should be overruled by something 
wiser. What is this wiser motive? We shall see. 

As for public spirit, it is rendered nugatory by the “ dif¬ 
ficulties in the way of its effective operation.” For ex¬ 
ample, it might suggest putting checks upon the fecundity 
of the poor and the vicious; and “ no measure of repression 
would be too severe,” in the case of criminals. The hint 
is broad. But unfortunately, you cannot induce legisla¬ 
tures to take such measures, owing to the pestiferous “ ten¬ 
der sentiments of man towards man.” It thus appears, 
that public-spirit, or Benthamism, is not strong enough to 
be the effective tutor of love, (I am skipping to another 
page), which must, therefore, be handed over to “ the mo¬ 
tives which animate men in the pursuit of wealth,” in which 
alone we can confide, and which “ are in the highest degree 
beneficent.” 2 Yes, in the “ highest degree ” without ex¬ 
ception are they beneficent to the being upon whom all their 
blessings are poured out, namely, the Self, whose “ sole 
object,” says the writer in accumulating wealth is his in- 

2 How can a writer have any respect for science, as such, who is 
capable of confounding with the scientific propositions of political econ¬ 
omy, which have nothing to say concerning what is “beneficent,” such 
brummagem generalisations as this? 


EVOLUTIONARY LOVE 


273 


dividual “ sustenance and enjoyment.” Plainly, the author 
holds the notion that some other motive might be in a higher 
degree beneficent even for the man’s self to be a paradox 
wanting in good sense. He seeks to gloze and modify his 
doctrine; but he lets the perspicacious reader see what his 
animating principle is; and when, holding the opinions I 
have repeated, he at the same time acknowledges that so¬ 
ciety could not exist upon a basis of intelligent greed alone, 
he simply pigeon-holes himself as one of the eclectics of 
inharmonious opinions. He wants his mammon flavored 
with a soupqon of god. 

The economists accuse those to whom the enunciation 
of their atrocious villainies communicates a thrill of horror 

**mmmm* *mm m mtmnm 

of being sentimentalists. It may be so: I willingly confess 
to having some tincture of sentimentalism in me, God be 
thanked! Ever since the French Revolution brought this 
leaning of thought into ill-repute, — and not altogether 
undeservedly, I must admit, true, beautiful, and good as 
that great movement was, — it has been the tradition to 
picture sentimentalists as persons incapable of logical 
thought and unwilling to look facts in the eyes. This tra¬ 
dition may be classed with the French tradition that an 
Englishman says godam at every second sentence, the 
English tradition that an American talks about “ Brit¬ 
ishers,” and the American tradition that a Frenchman 
carries forms of etiquette to an inconvenient extreme, in 
short with all those traditions which survive simply because 
the men who use their eyes and ears are few and far be¬ 
tween. Doubtless some excuse there was for all those 
opinions in days gone by; and sentimentalism, when it 



274 


LOVE AND CHANCE 


was the fashionable amusement to spend one’s evenings 
in a flood of tears over a woeful performance on a candle- 
litten stage, sometimes made itself a little ridiculous. But 
what after all is sentimentalism? It is an ism, a doctrine, 
namely, the doctrine that great respect should be paid to 
the natural judgments of the sensible heart. This is what 
sentimentalism precisely is; and I entreat the reader to 
consider whether to contemn it is not of all blasphemies the 
most degrading. Yet the nineteenth century has steadily 
contemned it, because it brought about the Reign of Ter¬ 
ror. That it did so is true. Still, the whole question is 
one of how much . The Reign of Terror was very bad; but 
now the Gradgrind banner has been this century long 
flaunting in the face of heaven, with an insolence to pro¬ 
voke the very skies to scowl and rumble. Soon a flash and 
quick peal will shake economists quite out of their com- 
placency, too late. The twentieth century, in its latter 
half, shall surely see the deluge-tempest burst upon the 
social order, — to clear upon a world as deep in ruin as 
that greed-philosophy has long plunged it into guilt. No 
post-thermidorian high jinks then! 

So a miser is a beneficent power in a community, is he? 
With the same reason precisely, only in a much higher de¬ 
gree, you might pronounce the Wall Street sharp to be a 
good angel, who takes money from heedless persons not 
likely to guard it properly, who wrecks feeble enterprises 
better stopped, and who administers wholesome lessons to 
unwary scientific men, by passing worthless checks upon 
them, — as you did, the other day, to me, my millionaire 
Master in glomery, when you thought you saw your way 


EVOLUTIONARY LOVE 


275 


to using my process without paying for it, and of so be¬ 
queathing to your children something to boast of their 
father about, — and who by a thousand wiles puts money 
at the service of intelligent greed„ in his own person. Ber¬ 
nard Mandeville, in his Fable of the Bees, maintains 
that private vices of all descriptions are public benefits, 
and proves it, too, quite as cogently as the economist proves 
his point concerning the miser. He even argues, with no 
slight force, that but for vice civilization would never 
have existed. In the same spirit, it has been strongly 
maintained and is to-day widely believed that all acts of 
charity and benevolence, private and public, go seriously 
to degrade the human race. 

The Origin of Species of Darwin merely extends 
politico-economical views of progress to the entire realm of 
animal and vegetable life. The vast majority of our con¬ 
temporary naturalists hold the opinion that the true cause 
of those exquisite and marvellous adaptations of nature 
for which, when I was a boy, men used to extol the divine 
wisdom is that creatures are so crowded together that those 
of them that happen to have the slightest advantage force 
those less pushing into situations unfavorable to multipli¬ 
cation or even kill them before they reach the age of re¬ 
production. Among animals, the mere mechanical indi¬ 
vidualism is vastly reenforced as a power making for good 
by the animal's ruthless greed. As Darwin puts it on his 
title-page, it is the struggle for existence; and he should 
have added for his motto: Every individual for himself, 
and the Devil take the hindmost! Jesus, in his sermon 
on the Mount, expressed a different opinion. 


276 


LOVE AND CHANCE 


Here, then, is the issue. The gospel of Christ says that 
progress comes from every individual merging his individu¬ 
ality in sympathy with his neighbors. On the other side, 
the conviction of the nineteenth century is that progress 
takes place by virtue of every individual’s striving for him¬ 
self with all his might and trampling his neighbor under 
foot whenever he gets a chance to do so. This may ac¬ 
curately be called the Gospel of Greed. 

Much is to be said on both sides. I have not concealed, 
I could not conceal, my own passionate predilection. Such 
a confession will probably shock my scientific brethren. 
Yet the strong feeling is in itself, I think, an argument of 
some weight in favor of the agapastic theory of evolu¬ 
tion, — so far as it may be presumed to bespeak the nor¬ 
mal judgment of the Sensible Heart. Certainly, if it were 
possible to believe in agapasm without believing it warmly, 
that fact would be an argument against the truth of the 
doctrine. At any rate, since the warmth of feeling exists, 
it should on every account be candidly confessed; especially 
since it creates a liability to onesidedness on my part 
against which it behooves my readers and me to be severally 
on our guard. 


SECOND THOUGHTS. IRENICA. 

Let us try to define the logical affinities of the different 
theories of evolution. Natural selection, as conceived by 
Darwin, is a mode of evolution in which the only positive 
agent of change in the whole passage from moner to man 
is fortuitous variation. To secure advance in a definite 

.. 

direction chance has to be seconded by some action that 


EVOLUTIONARY LOVE 


277 


shall hinder the propagation of some varieties or stimulate 
that of others. In natural selection, strictly so called, it 
is the crowding out of the weak. In sexual selection, it is 
the attraction of beauty, mainly. 

The Origin of Species was published toward the end 
of the year 1859. The preceding years since 1846 had been 
one of the most productive seasons, — or if extended so 
as to cover the great book we are considering, the most pro¬ 
ductive period of equal length in the entire history of 
science from its beginnings until now. The idea that chance 
begets order, which is one of the corner-stones of modern 
physics (although Dr. Carus considers it “ the weakest 
point in Mr. Peirce’s system,”) was at that time put into 
its clearest light. Quetelet had opened the discussion by his 
Letters on the Application of Probabilities to the Moral 
and Political Sciences, a work which deeply impressed 
the best minds of that day, and to which Sir John Herschel 
had drawn general attention in Great Britain. In 1857, the 
first volume of Buckle’s History of Civilisation had 
created a tremendous sensation, owing to the use he made of 
this same idea. Meantime, the “ statistical method ” had, 
under that very name, been applied with brilliant success 
to molecular physics. Dr. John Herapath, an English 
chemist, had in 1847 outlined the kinetical theory of gases 
in his Mathematical Physics; and the interest the theory 
excited had been refreshed in 1856 by notable memoirs by 
Clausius and Kronig. In the very summer preceding Dar¬ 
win’s publication, Maxwell had read before the British 
Association the first and most important of his researches 
on this subject. The consequence was that the idea that 


278 


LOVE AND CHANCE 


fortuitous events may result in a physical law, and further 
that this is the way in which those laws which appear to 
conflict with the principle of the conservation of energy 
are to be explained, had taken a strong hold upon the minds 
of all who were abreast of the leaders of thought. By such 
minds, it was inevitable that the Origin of Species, whose 
teaching was simply the application of the same principle 
to the explanation of another “ non-conservative ” action, 
that of organic development, should be hailed and wel¬ 
comed. The sublime discovery of the conservation of energy 
by Helmholtz in 1847, and that of the mechanical theory of 
heat by Clausius and by Rankine, independently, in 1850, 
had decidedly overawed all those who might have been 
inclined to sneer at physical science. Thereafter a belated 
poet still harping upon “ science peddling with the names 
of things ” would fail of his effect. Mechanism was now 
known to be all, or very nearly so. All this time, utilitari¬ 
anism, — that improved substitute for the Gospel, — was 
in its fullest feather; and was a natural ally of an indi¬ 
vidualistic theory. Dean Mansell’s injudicious advocacy 
had led to mutiny among the bondsmen of Sir William 
Hamilton, and the nominalism of Mill had profited ac¬ 
cordingly; and although the real science that Darwin was 
leading men to was sure some day to give a death-blow to 
the sham-science of Mill, yet there were several elements 
of the Darwinian theory which were sure to charm the 
followers of Mill. Another thing: anaesthetics had been in 
use for thirteen years. Already, people’s acquaintance with 
suffering had dropped off very much; and as a consequence, 
that unlovely hardness by which our times are so contrasted 


EVOLUTIONARY LOVE 


279 


with those that immediately preceded them, had already 
set in, and inclined people to relish a ruthless theory. The 
reader would quite mistake the drift of what I am saying 
if he were to understand me as wishing to suggest that 
any of those things (except perhaps Malthus) influenced 
Darwin himself. What I mean is that his hypothesis, while 
without dispute one of the most ingenious and pretty ever 
devised, and while argued with a wealth of knowledge, a 
strength of logic, a charm of rhetoric, and above all with 
a certain magnetic genuineness that was almost irresisti¬ 
ble, did not appear, at first, at all near to being proved; 
and to a sober mind its case looks less hopeful now than 
it did twenty years ago; but the extraordinarily favorable 
reception it met with was plainly owing, in large measure, * 
to its ideas being those toward which the age was favorably 
disposed, especially, because of the encouragement it gave 
to the greed-philosophy. 

Diametrically opposed to evolution by chance, are those 
theories which attribute all progress to an inward necessary 
principle, or other form of necessity. Many naturalists 
have thought that if an egg is destined to go through a 
certain series of embryological transformations, from which 
it is perfectly certain not to deviate, and if in geological 
time almost exactly the same forms appear successively, 
one replacing another in the same order, the strong pre¬ 
sumption is that this latter succession was as predeterminate 
and certain to take place as the former. So, Nageli, for 
instance, conceives that it somehow follows from the first 
law of motion and the peculiar, but unknown, molecular 
constitution of protoplasm, that forms must complicate 


280 


LOVE AND CHANCE 


themselves more and more. Kolliker makes one form 
generate another after a certain maturation has been ac¬ 
complished. Weismann, too, though he calls himself a 
Darwinian, holds that nothing is due to chance, but that 
all forms are simple mechanical resultants of the heredity 
from two parents. 3 It is very noticeable that all these dif¬ 
ferent sectaries seek to import into their science a mechani¬ 
cal necessity to which the facts that come under their ob¬ 
servation do not point. Those geologists who think that the 
variation of species is due to cataclysmic alterations of 
climate or of the chemical constitution of the air and water 
are also making mechanical necessity chief factor of 
evolution. 

Evolution by sporting and evolution by mechanical neces¬ 
sity are conceptions warring against one another. A third 
method, which supersedes their strife, lies enwrapped in 
the theory of Lamarck. According to his view, all that 
distinguishes the highest organic forms from the most 
rudimentary has been brought about by little hypertrophies 
or atrophies which have affected individuals early in their 
lives, and have been transmitted to their offspring. Such 
a transmission of acquired characters is of the general 
nature of habit-taking, and this is the representative and 
derivative within the physiological domain of the law of 
mind. Its action is essentially dissimilar to that of a physi¬ 
cal force; and that is the secret of the repugnance of such 
necessitarians as Weismann to admitting its existence. The 
Lamarckians further suppose that although some of the 

3 I am happy to find that Dr. Cams, too, ranks Weismann among the 
opponents of Darwin, notwithstanding his flying that flag. 


EVOLUTIONARY LOVE 


281 


modifications of form so transmitted were originally due to 
mechanical causes, yet the chief factors of their first produc¬ 
tion were the straining of endeavor and the overgrowth 
superinduced by exercise, together with the opposite actions. 
Now, endeavor, since it is directed toward an end, is es¬ 
sentially psychical, even though it be sometimes uncon¬ 
scious; and the growth due to exercise, as I argued in my 
last paper, follows a law of a character quite contrary to 
that of mechanics. 

Lamarckian evolution is thus evolution by the force of 
habit. — That sentence slipped off my pen while one of 
those neighbors whose function in the social cosmos seems 
to be that of an Interrupter, was asking me a question. Of 
course, it is nonsense. Habit is mere inertia, a resting on 
one’s oars, not a propulsion. Now it is energetic pro- 
jaculation (lucky there is such a word, or this untried 
hand might have been put to inventing one) by which in 
the typical instances of Lamarckian evolution the new 
elements of form are first created. Habit, however, forces 
them to take practical shapes, compatible with the struc¬ 
tures they affect, and in the form of heredity and other¬ 
wise, gradually replaces the spontaneous energy that sus¬ 
tains them. Thus, habit plays a double part; it serves to 
establish the new features, and also to bring them into 
harmony with the general morphology and function of the 
animals and plants to which they belong. But if the reader 
will now kindly give himself the trouble of turning back a 
page or two, he will see that this account of Lamarckian 
evolution coincides with the general description of the 
action of love, to which, I suppose, he yielded his assent. 


282 


LOVE AND CHANCE 


Remembering that all matter is really mind, remember¬ 
ing, too, the continuity of mind, let us ask what aspect 
Lamarckian evolution takes on within the domain of con¬ 
sciousness. Direct endeavor can achieve almost nothing. 
It is as easy by taking thought to add a cubit to one’s 
stature, as it is to produce an idea acceptable to any of 
the Muses by merely straining for it, before it is ready to 
come. We haunt in vain the sacred well and throne of 
Mnemosyne; the deeper workings of the spirit take place 
in their own slow way, without our connivance. Let but 
their bugle sound, and we may then make our effort, sure 
of an oblation for the altar of whatsoever divinity its savor 
gratifies. Besides this inward process, there is the operation 
of the environment, which goes to break up habits destined 
to be broken up and so to render the mind lively. Every¬ 
body knows that the long continuance of a routine of habit 
makes us lethargic, while a succession of surprises wonder¬ 
fully brightens the ideas. Where there is a motion, where 
history is a-making, there is the focus of mental activity, 
and it has been said that the arts and sciences reside within 
the temple of Janus, waking when that is open, but slum¬ 
bering when it is closed. Few psychologists have per¬ 
ceived how fundamental a fact this is. A portion of mind 
abundantly commissured to other portions works almost 
mechanically. It sinks to a condition of a railway junction. 
But a portion of mind almost isolated, a spiritual peninsula, 
or cul-de-sac, is like a railway terminus. Now mental 
commissures are habits. Where they abound, originality is 
not needed and is not found; but where they are 
in defect, spontaneity is set free. Thus, the first 


EVOLUTIONARY LOVE 


283 


step in the Lamarckian evolution of mind is the putting of 
sundry thoughts into situations in which they are free to 
play. As to growth by exercise, I have already shown, in 
discussing Man’s Glassy Essence, in last October’s 
Monist, what its modus operandi must be conceived to be, 
at least, until a second equally definite hypothesis shall 
have been offered. Namely, it consists of the flying 
asunder of molecules, and the reparation of the parts by 
new matter. It is, thus, a sort of reproduction. It takes 
place only during exercise, because the activity of proto¬ 
plasm consists in the molecular disturbance which is its 
necessary condition. Growth by exercise takes place also 
in the mind. Indeed, that is what it is to learn. But the 
most perfect illustration is the development of a philosophi¬ 
cal idea by being put into practice. The conception which 
appeared, at first, as unitary, splits up into special cases; 
and into each of these new thought must enter to make a 
practicable idea. This new thought, however, follows 
pretty closely the model of the parent conception; and thus 
a homogeneous development takes place. The parallel 
between this and the course of molecular occurrences is 
apparent. Patient attention will be able to trace all these 
elements in the transaction called learning. 

Three modes of evolution have thus been brought be¬ 
fore us; evolution by fortuitous variation, evolution by 
mechanical necessity, and evolution by creative love. We 
may term them tychastic evolution, or tychasm, anancastic 
evolution, or anancasm, and agapastic evolution, or aga- 
pasm. The doctrines which represent these as severally of 
principal importance, we may term tychasticism, anancas- 


284 


LOVE AND CHANCE 


ticism, and agapasticism. On the other hand the mere 
propositions that absolute chance, mechanical necessity, 
and the law of love, are severally operative in the cosmos, 
may receive the names of tychism, anancism, and agapism. 

All three modes of evolution are composed of the same 
general elements. Agapasm exhibits them the most clearly. 
The good result is here brought to pass, first, by the be¬ 
stowal of spontaneous energy by the parent upon the off¬ 
spring, and, second, by the disposition of the latter to catch 
the general idea of those about it and thus to subserve 
the general purpose. In order to express the relation 
that tychasm and anancasm bear to agapasm, let me bor¬ 
row a word from geometry. An ellipse crossed by a 
straight line is a sort of cubic curve; for a cubic is a curve 
which is cut thrice by a straight line; now a straight line 
might cut the ellipse twice and its associated straight line 
a third time. Still the ellipse with the straight line across 
it would not have the characteristics of a cubic. It would 
have, for instance, no contrary flexure, which no true cubic 
wants; and it would have two nodes, which no true cubic 
has. The geometers say that it is a degenerate cubic. Just 
so, tychasm and anancasm are degenerate forms of 
agapasm. 

Men who seek to reconcile the Darwinian idea with 
Christianity will remark that tychastic evolution, like the 
agapastic, depends upon a reproductive creation, the forms 
preserved being those that use the spontaneity conferred 
upon them in such wise as to be drawn into harmony with 
their original, quite after the Christian scheme. Very 
good! This only shows that just as love cannot have a 


EVOLUTIONARY LOVE 


285 


contrary, but must embrace what is most opposed to it, as a 
degenerate case of it, so tychasm is a kind of agapasm. 
Only, in the tychastic evolution progress is solely owing to 
the distribution of the napkin-hidden talent of the re¬ 
jected servant among those not rejected, just as ruined 
gamesters leave their money on the table to make those 
not yet ruined so much the richer. It makes the felicity 
of the lambs just the damnation of the goats, transposed 
to the other side of the equation. In genuine agapasm, 
on the other hand, advance takes place by virtue of a posi¬ 
tive sympathy among the created springing from continuity 
of mind. This is the idea which tychasticism knows not 
how to manage. 

The anancasticist might here interpose, claiming that 
the mode of evolution for which he contends agrees with 
agapasm at the point at which tychasm departs from it. 
For it makes development go through certain phases, having 
its inevitable ebbs and flows, yet tending on the whole to a 
foreordained perfection. Bare existence by this its destiny 
betrays an intrinsic affinity for the good. Herein, it must 
be admitted, anancasm shows itself to be in a broad accep- 
tion a species of agapasm. Some forms of it might easily 
be mistaken for the genuine agapasm. The Hegelian phil¬ 
osophy is such an anancasticism. With its revelatory re¬ 
ligion, with its synechism (however imperfectly set forth), 
with its “ reflection,” the whole idea of the theory is superb, 
almost sublime. Yet, after all, living freedom is practically 
omitted from its method. The whole movement is that 
of a vast engine, impelled by a vis a tergo, with a blind and 
mysterious fate of arriving at a lofty goal. I mean that 


286 


LOVE AND CHANCE 


such an engine it would be, if it really worked; but in point 
of fact, it is a Keely motor. Grant that it really acts as 
it professes to act, and there is nothing to do but accept the 
philosophy. But never was there seen such an example of 
a long chain of reasoning, — shall I say with a flaw in 
every link? — no, with every link a handful of sand, 
squeezed into shape in a dream. Or say, it is a pasteboard 
model of a philosophy that in reality does not exist. If we 
use the one precious thing it contains, the idea of it, in¬ 
troducing the tychism which the arbitrariness of its every 
step suggests, and make that the support of a vital free¬ 
dom which is the breath of the spirit of love, we may be 
able to produce that genuine agapasticism, at which Hegel 
was aiming. 


A THIRD ASPECT. DISCRIMINATION 

In the very nature of things, the line of demarcation be¬ 
tween the three modes of evolution is not perfectly sharp. 
That does not prevent its being quite real; perhaps it is 
rather a mark of its reality. There is in the nature of things 
no sharp line of demarcation between the three funda¬ 
mental colors, red, green, and violet. But for all that they 
are really different. The main question is whether three 
radically different evolutionary elements have been opera¬ 
tive; and the second question is what are the most striking 
characteristics of whatever elements have been operative. 

I propose to devote a few pages to a very slight examina¬ 
tion of these questions in their relation to the historical 
development of human thought. I first formulate for the 
reader’s convenience the briefest possible definitions of the 


EVOLUTIONARY LOVE 


287 


three conceivable modes of development of thought, dis¬ 
tinguishing also two varieties of anancasm and three of 
agapasm. The tychastic development of thought, then, 
will consist in slight departures from habitual ideas in dif¬ 
ferent directions indifferently, quite purposeless and quite 
unconstrained whether by outward circumstances or by 
force of logic, these new departures being followed by un¬ 
foreseen results which tend to fix some of them as habits 
more than others. The anancastic development of thought 
will consist of new ideas adopted without foreseeing whither 
they tend, but having a character determined by causes 
either external to the mind, such as changed circumstances 
of life, or internal to the mind as logical developments of 
ideas already accepted, such as generalizations. The aga- 
pastic development of thought is the adoption of certain 
mental tendencies, not altogether heedlessly, as in tychasm, 
nor quite blindly by the mere force of circumstances or of 
logic, as in anancasm, but by an immediate attraction for 
the idea itself, whose nature is divined before the mind 
possesses it, by the power of sympathy, that is, by virtue 
of the continuity of mind; and this mental tendency may 
be of three varieties, as follows: First, it may affect a 
whole people or community in its collective personality, 
and be thence communicated to such individuals as are in 
powerfully sympathetic connection with the collective 
people, although they may be intellectually incapable of 
attaining the idea by their private understandings or even 
perhaps of consciously apprehending it. Second, it may 
affect a private person directly, yet so that he is only enabled 
to apprehend the idea, or to appreciate its attractiveness, 


288 


LOVE AND CHANCE 


by virtue of his sympathy with his neighbors, under the in¬ 
fluence of a striking experience or development of thought. 
The conversion of St. Paul may be taken as an example of 
what is meant. Third, it may affect an individual, inde¬ 
pendently of his human affections, by virtue of an attraction 
it exercises upon his mind, even before he has comprehended 
it. This is the phenomenon which has been well called the 
divination of genius; for it is due to the continuity between 
the man’s mind and the Most High. 

Let us next consider by means of what tests we can dis¬ 
criminate between these different categories of evolution. 
No absolute criterion is possible in the nature of things, 
since in the nature of things there is no sharp line of de¬ 
marcation between the different classes. Nevertheless, 
quantitative symptoms may be found by which a sagacious 
and sympathetic judge of human nature may be able to 
estimate the approximate proportions in which the different 
kinds of influence are commingled. 

So far as the historical evolution of human thought has 
been tychastic, it should have proceeded by insensible or 
minute steps; for such is the nature of chances when so 
multiplied as to show phenomena of regularity. For ex¬ 
ample, assume that of the native-born white adult males 
of the United States in 1880, one-fourth part were below 
5 feet 4 inches in stature and one-fourth part above 5 feet 
8 inches. Then by the principles of probability, among the 
whole population, we should expect 

216 under 4 feet 6 inches, 216 above 6 feet 6 inches 


00 

T}- 

4 

“ 5 “ 

48 

“ 6 

44 

7 

U 

9 “ 

4 

a A u 

4 

9 

“ 6 

U 

8 

u 

less than 2 “ 

4 

“ 3 “ 

less than 2 

“ 6 

a 

9 

66 



EVOLUTIONARY LOVE 


289 


I set down these figures to show how insignificantly few 
are the cases in which anything very far out of the common 
run presents itself by chance. Though the stature of only 
every second man is included within the four inches be¬ 
tween 5 feet 4 inches and 5 feet 8 inches, yet if this interval 
be extended by thrice four inches above and below, it will 
embrace all our 8 millions odd of native-born adult white 
males (of 1880), except only 9 taller and 9 shorter. 

The test of minute variation, if not satisfied, absolutely 
negatives tychasm. If it is satisfied, we shall find that it 
negatives anancasm but not agapasm. We want a positive 
test, satisfied by tychasm, only. Now wherever we find 
men’s thought taking by imperceptible degrees a turn con¬ 
trary to the purposes which animate them, in spite of their 
highest impulses, there, we may safely conclude, there has 
been a tychastic action. 

Students of the history of mind there be of an erudition 
to fill an imperfect scholar like me with envy edulcorated 
by joyous admiration, who maintain that ideas when just 
started are and can be little more than freaks, since they 
cannot yet have been critically examined, and further that 
everywhere and at all times progress has been so gradual 
that it is difficult to make out distinctly what original step 
any given man has taken. It would follow that tychasm 
has been the sole method of intellectual development. I 
have to confess I cannot read history so; I cannot help 
thinking that while tychasm has sometimes been operative, 
at others great steps covering nearly the same ground and 
made by different men independently, have been mistaken 
for a succession of small steps, and further that students 


290 


LOVE AND CHANCE 


have been reluctant to admit a real entitative “ spirit ” of 
an age or of a people, under the mistaken and unscrutinized 
impression that they should thus be opening the door to wild 
and unnatural hypotheses. I find, on the contrary, that, 
however it may be with the education of individual minds, 
the historical development of thought has seldom been 
of a tychastic nature, and exclusively in backward and 
barbarizing movements. I desire to speak with the extreme 
modesty which befits a student of logic who is required to 
survey so very wide a field of human thought that he can 
cover it only by a reconnaissance, to which only the greatest 
skill and most adroit methods can impart any value at all; 
but, after all, I can only express my own opinions and not 
those of anybody else; and in my humble judgment, the 
largest example of tychasm is afforded by the history of 
Christianity, from about its establishment by Constantine, 
to, say, the time of the Irish monasteries, an era or eon of 
about 500 years. Undoubtedly the external circumstance 
which more than all others at first inclined men to accept 
Christianity in its loveliness and tenderness, was the fearful 
extent to which society was broken up into units by the un¬ 
mitigated greed and hard-heartedness into which the 
Romans had seduced the world. And yet it was that very 
same fact, more than any other external circumstance, that 
fostered that bitterness against the wicked world of which 
the primitive gospel of Mark contains not a single trace. 
At least, I do not detect it in the remark about the blas¬ 
phemy against the Holy Ghost, where nothing is said about 
vengeance, nor even in that speech where the closing lines of 
Isaiah are quoted, about the worm and the fire that feed 


EVOLUTIONARY LOVE 


291 


upon the “carcasses of the men that have transgressed 
against me.” But little by little the bitterness increases 
until in the last book of the New Testament, its poor dis¬ 
tracted author represents that all the time Christ was talk¬ 
ing about having come to save the world, the secret design 
was to catch the entire human race, with the exception of a 
paltry 144,000, and souse them all in a brimstone lake, 
and as the smoke of their torment went up forever and ever, 
to turn and remark, “ There is no curse any more.” Would 
it be an insensible smirk or a fiendish grin that should 
accompany such an utterance? I wish I could believe St. 
John did not write it; but it is his gospel which tells about 
the “ resurrection unto condemnation,” — that is of men’s 
being resuscitated just for the sake of torturing them; — 
and, at any rate, the Revelation is a very ancient composi¬ 
tion. One can understand that the early Christians were 
like men trying with all their might to climb a steep declivity 
of smooth wet clay; the deepest and truest element of 
their life, animating both heart and head, was universal 
love; but they were continually, and against their wills, 
slipping into a party spirit, every slip serving as a precedent, 
in a fashion but too familiar to every man. This party feel¬ 
ing insensibily grew until by about a.d. 330 the luster of 
the pristine integrity that in St. Mark reflects the whTe 
spirit of light was so far tarnished that Eusebius, (the Jared 
Sparks of that day), in the preface to his History, could an¬ 
nounce his intention of exaggerating everything that tended 
to the glory of the church and of suppressing whatever 
might disgrace it. His Latin contemporary Lactantius is 
worse, still; and so the darkling went on increasing until 


292 


LOVE AND CHANCE 


before the end of the century the great library of Alexan¬ 
dria was destroyed by Theophilus, 4 until Gregory the Great, 
two centuries later, burnt the great library of Rome, pro¬ 
claiming that “Ignorance is the mother of devotion,’ 5 
(which is true, just as oppression and injustice is the 
mother of spirituality), until a sober description of the 
state of the church would be a thing our not too nice news¬ 
papers would treat as “ unfit for publication.” All this 
movement is shown by the application of the test given 
above to have been tychastic. Another very much like 
it on a small scale, only a hundred times swifter, for the 
study of which there are documents by the library-full, 
is to be found in the history of the French Revolution. 

Anancastic evolution advances by successive strides 
with pauses between. The reason is that in this process 
a habit of thought having been overthrown is supplanted by 
the next strongest. Now this next strongest is sure to be 
widely disparate from the first, and as often as not is its 
direct contrary. It reminds one of our old rule of making 
the second candidate vice-president. This character, there¬ 
fore, clearly distinguishes anancasm from tychasm. The 
character which distinguishes it from agapasm is its pur¬ 
poselessness. But external and internal anancasm have to 
be examined separately. Development under the pressure 
of external circumstances, or cataclysmine evolution, 
is in most cases unmistakable enough. It has number¬ 
less degrees of intensity, from the brute force, the plain war, 
which has more than once turned the current of the world’s 
thought, down to the hard fact of evidence, or what has been 

* See Draper's History of Intellectual Development, chap. x. 


EVOLUTIONARY LOVE 


293 


taken for it, which has been known to convince men by 
hordes. The only hesitation than can subsist in the presence 
of such a history is a quantitative one. Never are external 
influences the only ones which affect the mind, and therefore 
it must be a matter of judgment for which it would scarcely 
be worth while to attempt to set rules, whether a given 
movement is to be regarded as principally governed from 
without or not. In the rise of medieval thought, I mean 
scholasticism and the synchronistic art developments, un¬ 
doubtedly the crusades and the discovery of the writings of 
Aristotle were powerful influences. The development of 
scholasticism from Roscellin to Albertus Magnus closely 
follows the successive steps in the knowledge of Aristotle. 
Prantl thinks that that is the whole story, and few men 
have thumbed more books than Carl Prantl. He has done 
good solid work, notwithstanding his slap-dash judgments. 
But we shall never make so much as a good beginning 
of comprehending scholasticism until the whole has been 
systematically explored and digested by a company of stu¬ 
dents regularly organized and held under rule for that pur¬ 
pose. But as for the period we are now specially consider¬ 
ing, that which synchronised the Romanesque architecture, 
the literature is easily mastered. It does not quite justify 
PrantPs dicta as to the slavish dependence of these authors 
upon their authorities. Moreover, they kept a definite 
purpose steadily before their minds, throughout all their 
studies. I am, therefore, unable to offer this period of 
scholasticism as an example of pure external anancasm, 
which seems to be the fluorine of the intellectual elements. 
Perhaps the recent Japanese reception of western ideas is 


294 


LOVE AND CHANCE 


the purest instance of it in history. Yet in combination 
with other elements, nothing is commoner. If the devel¬ 
opment of ideas under the influence of the study of external 
facts be considered as external anancasm, — it is on the 
border between the external and the internal forms, — it 
is, of course, the principal thing in modern learning. But 
Whewell, whose masterly comprehension of the history of 
science critics have been too ignorant properly to appreciate, 
clearly shows that it is far from being the overwhelmingly 
preponderant influence, even there. 

Internal anancasm, or logical groping, which advances 
upon a predestined line without being able to foresee whither 
it is to be carried nor to steer its course, this is the rule of 
development of philosophy. Hegel first made the world 
understand this; and he seeks to make logic not merely 
the subjective guide and monitor of thought, which was all 
it had been ambitioning before, but to be the very main¬ 
spring of thinking, and not merely of individual thinking but 
of discussion, of the history of the development of thought, 
of all history, of all development. This involves a positive, 
clearly demonstrable error. Let the logic in question be 
of whatever kind it may, a logic of necessary inference or 
a logic of probable inference (the theory might perhaps 
be shaped to fit either), in any case it supposes that logic is 
sufficient of itself to determine what conclusion follows 
from given premises; for unless it will do so much, it will 
not suffice to explain why an individual train of reasoning 
should take just the course it does take, to say nothing 
of other kinds of development. It thus supposes that from 
given premises, only one conclusion can logically be drawn, 


EVOLUTIONARY LOVE 


295 


and that there is no scope at all for free choice. That from 
given premises only one conclusion can logically be drawn, 
is one of the false notions which have come from logicians' 
confining their attention to that Nantucket of thought, the 
logic of non-relative terms. In the logic of relatives, it 
does not hold good. 

One remark occurs to me. If the evolution of history is 
in considerable part of the nature of internal anancasm, it 
resembles the development of individual men; and just as 
33 years is a rough but natural unit of time for individuals, 
being the average age at which man has issue, so there 
should be an approximate period at the end of which one 
great historical movement ought to be likely to be sup¬ 
planted by another. Let us see if we can make out any¬ 
thing of the kind. Take the governmental development of 
Rome as being sufficiently long and set down the principal 
dates. 

b.c. 753, Foundation of Rome. 
b.c. 510, Expulsion of the Tarquins. 
b.c. 27, Octavius assumes title Augustus. 
a.d. 476, End of Western Empire. 
a.d. 962, Holy Roman Empire. 
a.d. 1453, Fall of Constantinople. 

The last event was one of the most significant in history, 
especially for Italy. The intervals are 243, 483, 502, 486, 
491 years. All are rather curiously near equal, except the 
first which is half the others. Successive reigns of kings 
would not commonly be so near equal. Let us set down 
a few dates in the history of thought. 


296 


LOVE AND CHANCE 


b.c. 585, Eclipse of Thales. Beginning of Greek phi¬ 
losophy. 

a.d. 30, The crucifixion. 

a.d. 529, Closing of Athenian schools. End of Greek 
philosophy. 

a.d. 1125, (Approximate) Rise of the Universities of 
Bologna and Paris. 

a. d. 1543, Publication of the “ De Revolutionibus ” of 

Copernicus. Beginning of Modern Science. 

The intervals are 615, 499, 596, 418, years. In the history 
of metaphysics, we may take the following: 

b. c. 322, Death of Aristotle. 

a.d. 1274, Death of Aquinas. 

a.d. 1804, Death of Kant. 

The intervals are 1595 and 530 years. The former is about 
thrice the latter. 

From these figures, no conclusion can fairly be drawn. 
At the same time, they suggest that perhaps there may be 
a rough natural era of about 500 years. Should there be 
any independent evidence of this, the intervals noticed may 
gain some significance. 

The agapastic development of thought should, if it exists, 
be distinguished by its purposive character, this purpose 
being the development of an idea. We should have a direct 
agapic or sympathetic comprehension and recognition of it, 
by virtue of the continuity of thought. I here take it for 
granted that such continuity of thought has been sufficiently 
proved by the arguments used in my paper on the “ Law 
of Mind ” in The Monist of last July. Even if those argu¬ 
ments are not quite convincing in themselves, yet if they 


EVOLUTIONARY LOVE 


297 


are reenforced by an apparent agapasm in the history of 
thought, the two propositions will lend one another mutual 
aid. The reader will, I trust, be too well grounded in logic 
to mistake such mutual support for a vicious circle in reason¬ 
ing. If it could be shown directly that there is such an 
entity as the “ spirit of an age ” or of a people, and that 
mere individual intelligence will not account for all the 
phenomena, this would be proof enough at once of agapas- 
ticism and of synechism. I must acknowledge that I am 
unable to produce a cogent demonstration of this; but I 
am, I believe, able to adduce such arguments as will serve 
to confirm those which have been drawn from other facts. 
I believe that all the greatest achievements of mind have 
been beyond the powers of unaided individuals; and I find, 
apart from the support this opinion receives from synechistic 
considerations, and from the purposive character of many 
great movements, direct reason for so thinking in the sub¬ 
limity of the ideas and in their occurring simultaneously 
and independently to a number of individuals of no ex¬ 
traordinary general powers. The pointed Gothic architec¬ 
ture in several of its developments appears to me to be of 
such a character. All attempts to imitate it by modern 
architects of the greatest learning and genius appear flat 
and tame, and are felt by their authors to be so. Yet at the 
time the style was living, there was quite an abundance of 
men capable of producing works of this kind of gigantic 
sublimity and power. In more than one case, extant docu¬ 
ments show that the cathedral chapters, in the selection of 
architects, treated high artistic genius as a secondary con¬ 
sideration, as if there were no lack of persons able to supply 


LOVE AND CHANCE 


298 

that; and the results justify their confidence. Were indi¬ 
viduals in general, then, in those ages possessed of such lofty 
natures and high intellect? Such an opinion would break 
down under the first examination. 

How many times have men now in middle life seen great 
discoveries made independently and almost simultaneously! 
The first instance I remember was the prediction of a planet 
exterior to Uranus by Leverrier and Adams. One hardly 
knows to whom the principle of the conservation of energy 
ought to be attributed, although it may reasonably be con¬ 
sidered as the greatest discovery science has ever made. 
The mechanical theory of heat was set forth by Rankine 
and by Clausius during the same month of February, 1850; 
and there are eminent men who attribute this great step 
to Thomson. 5 The kinetical theory of gases, after being 
started by John Bernoulli and long buried in oblivion, was 
reinvented and applied to the explanation not merely of the 
laws of Boyle, Charles, and Avogadro, but also of diffusion 
and viscosity, by at least three modern physicists separately. 
It is well known that the doctrine of natural selection was 
presented by Wallace and by Darwin at the same meeting 
of the British Association; and Darwin in his “ Historical 
Sketch ” prefixed to the later editions of his book shows 
that both were anticipated by obscure forerunners. The 
method of spectrum analysis was claimed for Swan as well 
as for Kirchhoff, and there were others who perhaps had 
still better claims. The authorship of the Periodical Law 
of the Chemical Elements is disputed between a Russian, 

5 Thomson, himself, in his article Heat in the Encyclopedia Britannica, 
never once mentions the name of Clausius. 


EVOLUTIONARY LOVE 


299 


a German, and an Englishman; although there is no room 
for doubt that the principal merit belongs to the first. These 
are nearly all the greatest discoveries of our times. It is 
the same with the inventions. It may not be surprising 
that the telegraph should have been independently made by 
several inventors, because it was an easy corollary from 
scientific facts well made out before. But it was not so 
with the telephone and other inventions. Ether, the first 
anaesthetic, was introduced independently by three different 
New England physicians. Now ether had been a common 
article for a century. It had been in one of the pharma- 
' copoeias three centuries before. It is quite incredible that 
its anaesthetic property should not have been known; it 
was known. It had probably passed from mouth to ear 
as a secret from the days of Basil Valentine; but for long 
it had been a secret of the Punchinello kind. In New 
England, for many years, boys had used it lor amusement. 
Why then had it not been put to its serious use? No reason 
can be given, except that the motive to do so was not strong 
enough. The motives to doing so could only have been 
desire for gain and philanthropy. About 1846, the date of 
the introduction, philanthropy was undoubtedly in an un¬ 
usually active condition. That sensibility, or sentimental¬ 
ism, which had been introduced in the previous century, 
had undergone a ripening process, in consequence of which, 
though now less intense than it had previously been, it was 
more likely to influence unreflecting people than it had ever 
been. All three of the ether-claimants had probably been 
influenced by the desire for gain; but nevertheless they were 
certainly not insensible to the agapic influences. 


3°° 


LOVE AND CHANCE 


I doubt if any of the great discoveries ought, properly, 
to be considered as altogether individual achievements; and 
I think many will share this doubt. Yet, if not, what an 
argument for the continuity of mind, and for agapasticism 
is here! I do not wish to be very strenuous. If thinkers 
will only be persuaded to lay aside their prejudices and 
apply themselves to studying the evidences of this doctrine, 
I shall be fully content to await the final decision. 


Supplementary Essay 
THE PRAGMATISM OF PEIRCE 

BY 

John Dewey 

The term pragmatism was introduced into literature in the 
opening sentences of Professor James’s California Union address 
in 1898. The sentences run as follows: “ The principle of 
pragmatism, as we may call it, may be expressed in a variety 
of ways, all of them very simple. In the Popular Science 
Monthly for January, 1878, Mr. Charles S. Peirce introduces it 
as follows:” etc. The readers who have turned to the volume 
referred to have not, however, found the word there. From 
/ other sources we know that the name as well as the idea was 
furnished by Mr. Peirce. The latter has told us that both the 
word and the idea were suggested to him by a reading of Kant, 
the idea by the Critique oj Pure Reason , the term by the 
“Critique of Practical Reason.” 1 The article in the Monist 
gives such a good statement of both the idea and the reason for 
selecting the term that it may be quoted in extenso. Peirce sets 
out by saying that with men who work in laboratories, the habit 
of mind is molded by experimental work much more than they 
are themselves aware. “ Whatever statement you may make to 
him, he [the experimentalist] will either understand as meaning 
that if a given prescription for an experiment ever can be and 
ever is carried out in act, an experience of a given description 
will result, or else he will see no sense at all in what you say.” 
Having himself the experimental mind and being interested in 
methods of thinking, “ he framed the theory that a conception , 
that is, the rational purport of a word or other expression, lies 

1 See article on “ Pragmatism,” in Baldwin’s Dictionary, Vol. 2., p. 
322, and the Monist, Vol. 15, p. 162. 


302 


THE PRAGMATISM OF PEIRCE 


exclusively in its bearing upon the conduct of life; so that, 
since obviously nothing that might not result from experiment 
can have any direct bearing upon conduct, if one can define ac¬ 
curately all the conceivable experimental phenomena which the 
affirmation or denial of a concept could imply, one will have 
therein a complete definition of the concept, and there is abso¬ 
lutely nothing more in it. For this doctrine, he invented the 
name pragmatism” 

After saying that some of his friends wished him to call the 
doctrine practicism or practicalism, he says that he had learned 
philosophy from Kant, and that to one “ who still thought in 
Kantian terms most readily, praktisch and pragmatisch were as 
far apart as the two poles, the former belonging to a region of 
thought where no mind of the experimentalist type can ever 
make sure of solid ground under his feet, the latter expressing 
relation to some definite human purpose. Now quite the most 
striking feature of the new theory was its recognition of an in¬ 
separable connection between rational cognition and human 
purpose.” 2 

From this brief statement, it will be noted that Peirce con¬ 
fined the significance of the term to the determination of the 
meaning of terms, or better, propositions; the theory was not, of 
itself, a theory of the test, or the truth, of propositions. Hence 
the title of his original article: How to Make Ideas Clear. In 
his later writing, after the term had been used as a theory of 
truth, — he proposed the more limited “ pragmaticism ” to 
designate his original specific meaning. 3 But even with respect 
to the meaning of propositions, there is a marked difference 
between his pragmaticism and the pragmatism of, say, James. 
Some of the critics (especially continental) of the latter would 
have saved themselves some futile beating of the air, if they 
had reacted to James’s statements instead of to their own as- 

2 Kant discriminates the laws of morality, which are a priori, from 
rules of skill, having to do with technique or art, and counsels of prudence, 
having to do with welfare. The latter he calls pragmatic; the a priori 
laws practical. See Metaphysics of Morals, Abbott’s trans., pp. 33 and 34. 

3 See the article in the Monist already mentioned, and another one 
in the same volume, p. 481, “The Issues of Pragmaticism.” 


THE PRAGMATISM OF PEIRCE 


303 


sociations with the word “ pragmatic.” Thus James says in his 
California address: “ The effective meaning of any philosophic 
proposition can always be brought down to some particular con¬ 
sequence, in our future practical experience, whether active or 
passive; the point lying rather in the fact that the experience 
must be particular, than in the fact that it must be active” 
(Italics mine.) 

Now the curious fact is that Peirce puts more emphasis upon 
practise (or conduct) and less upon the particular; in fact, he 
transfers the emphasis to the general. The following passage is 
worth quotation because of the definiteness with which it identi¬ 
fies meaning with both the future and with the general. “ The 
rational meaning of every proposition lies in the future. How 
so? The meaning of a proposition is itself a proposition. In¬ 
deed, it is no other than the very proposition of which it is the 
meaning: it is a translation of it. But of the myriads of forms 
into which a proposition may be translated, which is that one 
which is to be called its very meaning? It is, according to the 
pragmaticist, that form in which the proposition becomes ap¬ 
plicable to human conduct, not in these or those special cir¬ 
cumstances nor when one entertains this or that special design, 
but that form which is most applicable to self-control under 
every situation and to every purpose.” Hence, “ it must be 
simply the general description of all the experimental phenomena 
which the assertion of the proposition virtually predicts.” Or, 
paraphrasing, pragmatism identifies meaning with formation 
of a habit, or way of acting having the greatest generality pos¬ 
sible, or the widest range of application to particulars. Since 
habits or ways of acting are just as real as particulars, it is com¬ 
mitted to a belief in the reality of “ universal.” Hence it is 
not a doctrine of phenomenalism, for while the richness of phe¬ 
nomena lies in their sensuous quality, pragmatism does not in¬ 
tend to define these (leaving them, as it were, to speak for 
themselves), but “eliminates their sential element, and en¬ 
deavors to define the rational purport, and this it finds in the 
purposive bearing of the word or proposition in question,” 
Moreover, not only are generals real, but they are physically 


304 


THE PRAGMATISM OF PEIRCE 


efficient. The meanings “ the air is stuffy ” and “ stuffy air is 
unwholesome ” may determine, for example, the opening of the 
window. Accordingly on the ethical side, “ the pragmaticist does 
not make the summum bonum to consist in action, but makes 
it to consist in that process of evolution whereby the existent 
comes more and more to embody those generals . . . ; in other 
words, becomes, through action an embodiment of rational pur¬ 
ports or habits generalized as widely as possible .” 4 

The passages quoted should be compared with what Peirce 
has to say in the Baldwin Dictionary article. There he says 
that James’s doctrine seems to commit us to the belief “ that 
the end of man is action — a stoical maxim which does not com¬ 
mend itself as forcibly to the present writer at the age of sixty 
as it did at thirty. If it be admitted, on the contrary, that 
action wants an end, and that the end must be something of a 
general description, then the spirit of the maxim itself . . . 
would direct us toward something different from practical facts, 
namely, to general ideas. . . . The only ultimate good which 
the practical facts to which the maxim directs attention can 
subserve is to further the development of concrete reasonableness. 

. . . Almost everybody will now agree that the ultimate good 
lies in the evolutionary process in some way. If so, it is not 
in individual reactions in their segregation, but in something 
general or continuous. Synechism is founded on the notion that 
the coalescence, the becoming continuous, the becoming gov¬ 
erned by laws, the becoming instinct with general ideas, are 
but phases of one and the same process of the growth of reason¬ 
ableness. This is first shown to be true with mathematical 
exactitude in the field of logic, and is thence inferred to hold 
good metaphysically. It is not opposed to pragmaticism . . . 
but includes that procedure as a step.” 

Here again we have the doctrine of pragmaticism as a doc¬ 
trine that meaning or rational purport resides in the setting up 

of habits or generalized methods, a doctrine passing over into 

* 

4 It is probably fair to see here an empirical rendering of the Kantian 
generality of moral action, while the distinction and connection of “ ra¬ 
tional purport ” and “ sensible particular ” have also obvious Kantian 
associations. 


THE PRAGMATISM OF PEIRCE 


305 


the metaphysics of synechism. It will be well now to recur 
explicitly to Peirce’s earlier doctrine which he seems to qualify 

— although, as he notes, he upheld the doctrine of the reality 
of generals even at the earlier period. Peirce sets out, in his 
article on the “ Fixation of Belief,” with the empirical differ¬ 
ence of doubt and belief expressed in the facts that belief deter¬ 
mines a habit while doubt does not, and that belief is calm 
and satisfactory while doubt is an uneasy and dissatisfied state 
from which we struggle to emerge; to attain, that is, a state of 
belief, a struggle which may be called inquiry. The sole object 
of inquiry is the fixation of belief. The scientific method of fixa¬ 
tion has, however, certain rivals: one is that of “tenacity” — 
constant reiteration, dwelling upon everything conducive to the 
belief, avoidance of everything which might unsettle it — the 
will to believe. The method breaks down in practice because 
of man’s social nature; we have to take account of contrary 
beliefs in others, so that the real problem is to fix the belief of 
the community; for otherwise our own belief is precariously 
exposed to attack and doubt. Hence the resort to the method 
of authority. This method breaks down in time by the fact 
that authority can not fix all beliefs in all their details, and 
because of the conflict which arises between organized traditions. 
There may then be recourse to what is “ agreeable to reason ” 

— a method potent in formation of taste and in esthetic produc¬ 
tions and in the history of philosophy, — but a method which 
again fails to secure permanent agreements in society, and so 
leaves individual belief at the mercy of attack. Hence, finally, 
recourse to science, whose fundamental hypothesis is this: 
“ There are real things, whose characters are entirely indepen¬ 
dent of our opinions about them; those realities affect our senses 
according to regular laws, and ... by taking advantage of the 
laws of perception, we can ascertain by reasoning how things 
really are, and any man if he have sufficient experience and rea¬ 
son enough about it, will be led to the one true conclusion.” 5 

It will be noted that the quotation employs the terms 
“ reality ” and “ truth,” while it makes them a part of the state- 


6 P. 26. 


306 


THE PRAGMATISM OF PEIRCE 


ment of the hypothesis entertained in scientific procedure. Upon 
such a basis, what meanings attach to the terms “ reality ” and 
“ truth ” ? Since they are general terms, their meanings must be 
determined on the basis of the effects, having practical bearings, 
which the object of our conception has. Now the effect which 
real things have is to cause beliefs; beliefs are then the conse¬ 
quences which give the general term reality a “ rational purport.” 
And on the assumption of the scientific method, the distinguishing 
character of the real object must be that it tends to produce a 
single universally accepted belief. “ All the followers of science 
are fully persuaded that the processes of investigation, if only 
pushed far enough, will give one certain solution to every ques¬ 
tion to which they can be applied.” “ This activity of thought 
by which we are carried, not where we wish, but to a foreor¬ 
dained goal, is like the operation of destiny. . . . This great 
law is embodied in the conception of truth and reality. The 
opinion which is fated to be ultimately agreed to by all who 
investigate, is what we mean by the truth, and the object repre¬ 
sented in this opinion is the real.” 6 In a subsequent essay 
(on the “ Probability of Induction ”) Peirce expressly draws 
the conclusion which follows from this statement; viz., that this 
conception of truth and reality makes everything depend upon 
the character of the methods of inquiry and inference by which 
conclusions are reached. “ In the case of synthetic inferences 
we know only the degree of trustworthiness of our proceeding. 
As all knowledge comes from synthetic inference, we must also 
infer that all human certainty consists merely in our knowing 
that the processes by which our knowledge has been derived 
are such as must generally have led to true conclusions ” 7 — 
true conclusions, once more, being those which command the 
agreement of competent inquiries. 

Summing up, we may say that Peirce’s pragmaticism is a 
doctrine concerning the meaning, conception, or rational pur¬ 
port of objects, namely, that these consist in the “ effects, which 
might conceivably have practical bearings, we conceive the ob- 


6 P. 56 - 57 - 


7 P. 105. 


THE PRAGMATISM OF PEIRCE 


30 ? 


ject of our conception to have. Then, our conception of these 
effects is the whole of our conception of the object.” 8 “ Our 
idea of anything is our idea of its sensible effects,” and if we have 
any doubt as to whether we really believe the effects to be sensi¬ 
ble or no, we have only to ask ourselves whether or no we should 
act any differently in their presence. In short, our own responses 
to sensory stimuli are the ultimate, or testing, ingredients in our 
conception of an object. In the literal sense of the word pragma¬ 
tist, therefore, Peirce is more of a pragmatist than James. 

He is also less of a nominalist. That is to say, he emphasizes 
much less the particular sensible consequence, and much more 
the habit, the generic attitude of response, set up in consequence 
of experiences with a thing. In the passage in the Dictionary 
already quoted he speaks as if in his later life he attached less 
importance to action, and more to “ concrete reasonableness ” 
than in his earlier writing. It may well be that the relative em¬ 
phasis had shifted. But there is at most but a difference of 
emphasis. For in his later doctrine, concrete rationality means a 
change in existence brought about through action, and through 
action which embodies conceptions whose own specific existence 
consists in habitual attitudes of response. In his earlier writing, 
the emphasis upon habits, as something generic, is explicit. 
“What a thing means is simply what habits it involves.” 9 
More elaborately, “ Induction infers a rule. Now the belief of 
a rule is a habit. That a habit is a rule, active in us, is evident. 
That every belief is of the nature of a habit, in so far as it is 
of a general character, has been shown in the earlier papers of 
this series.” 10 

The difference between Peirce and James which next strikes 
us is the greater emphasis placed by the former upon the method 
of procedure. As the quotations already made show, everything 
ultimately turned, for Peirce, upon the trustworthiness of the 
procedures of inquiry. Hence his high estimate of logic, as com¬ 
pared with James — at least James in his later days. Hence also 


8 P. 45 . 


9 P. 43 . 


i° P. 151 . 


308 


THE PRAGMATISM OF PEIRCE 


his definite rejection of the appeal to the Will to Believe — 
under the form of what he calls the method of tenacity. Closely 
associated with this is the fact that Peirce has a more explicit 
dependence upon the social factor than has James. The appeal 
in Peirce is essentially to the consensus of those who have in¬ 
vestigated, using methods which are capable of employment by 
all. It is the need for social agreement, and the fact that in its 
absence “ the method of tenacity ” will be exposed to disin¬ 
tegration from without, which finally forces upon mankind the 
wider and wider utilization of the scientific method. 

Finally, both Peirce and James are realists. The reasonings of 
both depend upon the assumption of real things which really 
have effects or consequences. Of the two, Peirce makes clearer 
the fact that in philosophy at least we are dealing with the 
conception of reality, with reality as a term having rational pur¬ 
port, and hence with something whose meaning is itself to be 
determined in terms of consequences. That “ reality ” means 
the object of those beliefs which have, after prolonged and 
cooperative inquiry, becomes stable, and “ truth ” the quality of 
these beliefs, is a logical consequence of this position. Thus 
while “ we may define the real as that whose characters are 
independent of what anybody may think them to be ... it 
would be a great mistake to suppose that this definition makes 
the idea of reality perfectly clear.” 11 For it is only the out¬ 
come of persistent and conjoint inquiry which enables us to give 
intelligible meaning in the concrete to the expression “ char¬ 
acters independent of what anybody may think them to be.” 
(This is the pragmatic way out of the egocentric predicament.) 
And while my purpose is wholly expository I can not close with¬ 
out inquiring whether recourse to Peirce would not have a most 
beneficial influence in contemporary discussion. Do not a large 
part of our epistemological difficulties arise from an attempt to 
define the “ real ” as something given prior to reflective inquiry 
instead of as that which reflective inquiry is forced to reach and 
to which when it is reached belief can stably cling? 


11 P. 53- 


BIBLIOGRAPHY OF PEIRCE’S PUBLISHED 

WRITINGS 

I. Writings of General Interest. 1 

A. Three papers in the Journal of Speculative Philosophy, Vol. 2 

(1868). 

1. “ Questions Concerning Certain Faculties Claimed for 

Man,” pp. 103-114. 

2. “ Some Consequences of Four Incapacities,” pp. 140-157. 

3. “ Ground of Validity of the Laws of Logic,” pp. 193-208. 

These three papers, somewhat loosely connected, deal mainly with the 

philosophy of discursive thought. The first deals with our power of in¬ 
tuition, and holds that “ every thought is a sign.” The second, one of the 
most remarkable of Peirce’s writings, contains an acute criticism of the 
Cartesian tradition and a noteworthy argument against the traditional 
emphasis on “ images ” in thinking. The third contains, inter alia, a 
refutation of Mill’s indictment of the syllogism. The same volume of the 
Journal contains two unsigned communications on Nominalism and on the 
Meaning of Determined. 

B. Review of Fraser’s “ Berkeley,” in the North American Review, 

Vol. 113 (1871), pp. 449-472. 

This paper contains an important analysis on medieval realism, and of 
Berkeley’s nominalism. (A Scotist realism continues to distinguish Peirce’s 
work after this.) 

C. “ Illustrations of the Logic of Science,” in Popular Science 

Monthly, Vols. 12-13 (1877-1878). Reprinted in Pt. I 
of this volume. The first and second papers were also 
published in the Revue Philosophique, Vols. 6-7 (1879). 

D. Ten papers in the Monist, Vols. 1-3 (1891-1893), and 15-16 

(1905-1906). The first five are reprinted in Pt. II of this 
volume. 

The sixth paper, “ Reply to the Necessitarians,” Vol. 3, pp. 526-570, is 
an answer to the criticism of the foregoing by the editor of the Monist, 
Vol. 2, pp. 56off.; cf. Vol. 3, pp. 68ff. and 57iff., and McCrie, “The Issues 
of Synechism,” Vol. 3, pp. 38off. 

1 The following classification is arbitrary, as some of Peirce’s most sig¬ 
nificant reflections occur in papers under headings II. and III. It may, 
however, be useful. 


309 


310 


BIBLIOGRAPHY 


7. “What Pragmatism Is?” Vol. 15, pp. 161-181. 

8. “The Issues of Fragmaticism,” Vol. 15, pp. 481-499. 

9. “Mr. Peterson’s Proposed Discussion,” Vol. 16, pp. 147^- 

10. “ Prolegomena to an Apology for Pragmaticism,” Vol. 16, 

pp. 492-S46. 

The last four papers develop Peirce’s thought by showing its agreement 
and disagreement with the pragmatism of James and Schiller. The last 
paper contains his Method of Existential Graphs. 

E. “The Reality of God,” in the Hibbert Journal, Vol. 7 (1908), 

pp. 96-112. (This article contains brief indications of many 
of Peirce’s leading ideas.) 

F. Six Papers in the Open Court, Vols. 6-7 (1893). 

1. “ Pythagorics” (on the Pythagorean brotherhood), pp. 

3375 - 3377 - 

2. “Dmesis” (on charity towards criminals), pp. 3399-3402. 

3. “The Critic of Arguments (I.), Exact Thinking,” pp. 3391- 

3394 - 

4. “The Critic of Arguments (II.), The Reader is Introduced 

to Relatives,” pp. 3415-3419. (The last two contain a 
very clear succinct account of the general character of 
Peirce’s logic.) 

5. “What is Christian Faith?” pp. 3743-3745. 

6. “The Marriage of Religion and Science,” pp. 3559-3560. 

G. Articles in Baldwin’s “Dictionary of Philosophy”: Individual, 

kind, matter and form, possibility, pragmatism, priority, 
reasoning, sign, scientific method, sufficient reason, syne- 
chism, and uniformity. 

H. “ Pearson’s Grammar of Science,” in Popular Science Monthly, 

Vol. 58 (1901), pp. 296-306. (A critique of Pearson’s 
conceptualism and of his utilitarian view as to the aim of 
science.) 

II. Writings of Predominantly Logical Interest. 

A. Five Papers on Logic, read before the American Academy of 
Arts and Sciences. Published in the Proceedings of the 
Academy, Vol. 7 (1867). 

1. “On an Improvement in Boole’s Calculus of Logic,” pp. 

250-261. (Suggests improvements in Boole’s logic, es- 
✓ pecially in the representation of particular propositions. 
The association of probability with the notion of rela¬ 
tive frequency became a leading idea of Peirce’s 
thought.) 

2. “On the Natural Classification of Arguments,” pp. 261- 

287. (A suggestive distinction between the leading 
principle and the premise of an argument. Contains 
also an interesting note (pp. 283-2S4) denying the posi- 


BIBLIOGRAPHY 


3 11 

tivistic maxim that, “no hypothesis is admissible which 
is not capable of verification by direct observation.”) 

3. “ On a New List of Categories,” pp. 287-298. The cate¬ 

gories are: Being, Quality (Reference to a Ground), 
Relation (Reference to a Correlate), Representation 
(Reference to an Interpretant), Substance. “Logic 
has for its subject-genus all symbols and not merely 
concepts.” Symbols include terms, propositions, and 
arguments. 

4. “Upon the Logic of Mathematics,” pp. 402-412. “There 

are certain general propositions from which the truths 
of mathematics follow syllogistically.” 

5. “Upon Logical Comprehension and Extension,” pp. 416- 

432. (Interesting historical references to the use of 
these terms and an attack on the supposed rule as to 
their inverse proportionality.) 

B. “ Description of a Notation for the Logic of Relations,” in 

Memoires of the American Academy , Vol. 9 (1870), pp. 
317-378. (Shows the relation of inclusion between classes 
to be more fundamental than Boole’s use of equality. Ex¬ 
tends the.Booleian calculus to DeMorgan’s logic of relative 
terms.) 

C. “ On the Algebra of Logic,” American Journal of Mathematics, 

Vol. 3 (1880), pp. 15-57. (Referred to by Schroeder as 
Peirce’s Hauptwerk in “ Vorlesungen liber die Algebra der 
Logik,” Vol. 1., p. 107.) 

D. “ On the Logic of Number,” American Journal of Mathematics, 

Vol. 4 (1881), pp. 85-95. 

E. “ Brief Description of the Algebra of Relatives,” Reprinted from 

??, pp. 1-6. 

F. “ On the Algebra of Logic: A Contribution to the Philosophy of 

Notation,” American Journal of Mathematics, Vol 7 (1884), 
pp. 180-202. 

G. “ A Theory of Probable Inference ” and notes “ On a Limited 

Universe of Marks ” and on the “ Logic of Relatives ” in 
“Studies in Logic by members of the Johns Hopkins 
University,” Boston, 1883, pp. 126-203. 

H. “The Regenerated Logic,” Monist, Vol. 7, pp. 19-40. 

“The Logic of Relatives,” Monist, Vol. 7, pp. 161-217. (An 
elaborate development of his own logic of relatives, by way 
of review of Schroeder’s book.) 

I . Miscellaneous Notes, etc. 

1. Review of Venn’s “Logic of Chance,” North American 

Review, July, 1867. 

2. “ On the Application of Logical Analysis to Multiple Al- 


3 12 


BIBLIOGRAPHY 


gebra,” Proceedings of the American Academy, Vol. 10 
(1875), PP- 392 - 394 - 

3. “ Note on Grassman’s ‘ Calculus of Extension,’ ” Proceed¬ 

ings of the American Academy, Vol. 13 (1878), pp. 115- 
116. 

4. “Note on Conversion,” Mind, Vol. 1, p. 424. 

5. Notes and Additions to Benjamin Peirce’s “ Linear Asso¬ 

ciative Algebra,” American Journal of Mathematics , 
Vol. 4 (1881), pp. 92ft., especially pp. 221-229. 

6. “ Logical Machines,” American Journal of Psychology, 

Vol. 1 (1888). 

7. “Infinitesimals,” Science, Vol. n (1900), p. 430. 

8. “ Some Amazing Mazes,” Monist, Vol. 18 (April and July, 

1908), and Vol. 19 (Jan., 1909). 

9. “On Non-Aristotelian Logic” (Letter), Monist, Vol. 20. 

J. A Syllabus of Certain Topics of Logic. 1903. Boston. Alfred 

Mudge & Son (a four page brochure). 

K. Articles in Baldwin’s “Dictionary of Philosophy” on: laws of 

thought, leading principle, logic (exact and symbolic), 
modality, negation, predicate and predication, probable in¬ 
ference, quality, quantity, relatives, significant, simple, sub¬ 
ject, syllogism, theory, truth and falsity universal, universe, 
validity, verification, whole and parts. 

III. Researches in the Theory and Methods of Measurement. 

A. General and Astronomic. 

1. “On the Theory of Errors of Observation,” Report of the 

Superintendent of the U. S. Coast Survey for 1870, pp. 
220-224. 

2. “Note on the Theory of Economy of Research,” Report 

of the U. S . Coast Survey for 1876, pp. 197-201. (This 
■v paper deals with the relation between the utility and 
the cost of diminishing the probable error.) 

3. “Apparatus for Recording a Mean of Observed Times,” 

U. S. Coast Survey, 1877. Appendix No. 15 to Report 
of 1875. 

4. “Ferrero’s Metodo dei Minimi Quadrati,” American Jour¬ 

nal of Mathematics, Vol. 1 (1878), pp. 55-63. 

5. “ Photometric Researches,” Annals of the Astronomical 

Observatory of Harvard College, Vol. 9 (1878), pp. 1- 
181. 

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3H 


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Note on the American Journal of Mathematics. Vol. 29, No. 756. 

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Ribot, Th., The Psychology of Attention, 1890. Vol. 50, No. 1303. 
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Comte, A. (F. Harrison, editor), The New Calendar of Great Men, 1892. 
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Buckley, Arabella B., Moral Teachings of Science, 1892. Vol. 54, No. 1405. 
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Mach, E. (Translator: T. J. McCormack), The Science of Mechanics, 
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Ritchie, D. G., Darwin and Hegel, 1893. Vol. 57, No. 1482. 

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Scott, Sir Walter, Familiar Letters of Sir Walter Scott. Vol. 58, No. 1493. 
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Forsyth, A. R., Theory of Functions of a Complex Variable, 1893; and 
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A Short Sketch of Helmholtz, Sept. 13, 1894. Vol. 59, No. 1524. 
Windelband, W. (Translator: J. H. Tufts), A History of Philosophy; and 
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Watson, J., Comte, Mill, and Spencer, 1895. Vol. 60, No. 1554. 

Jones, H., A Critical Account of the Philosophy of Lotze, 1895; and Eber- 
hard, V., Die Grundbegriffe der ebenen Geometrie, 1895; and Klein, 
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Benjamin, P., The Intellectual Rise in Electricity, 1895. Vol. 62, No. 1592. 

Baldwin, J. M., The Story of the Mind, 1898. Vol. 67, No. 1737. 

Darwin, G. H., The Tides and Kindred Phenomena in the Solar System, 
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Marshall, H. R., Instinct and Reason, 1898. Vol. 68, No. 1774. 

Britten, F. J., Old Clocks and Watches and their Makers, 1899. Vol. 69, 
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Renouvier, Ch., et Prat, L. La Nouvelle Monadologie, 1899. Vol. 69, 
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Mackintosh, R., From Comte to Benjamin Kidd, 1899; and Moore, J. H., 
Better-World Philosophy, 1899. Vol. 69, No. 1784. 

Ford, P. L., The Many-sided Franklin, 1899. Vol. 69, No. 1793. 

Avenel, G. d’, Le Mecanisme de la vie moderne, 1900. Vol. 70, No. 1805. 

Reid, W., Memoirs and Correspondence of Lyon Playfair, 1899. Vol. 70, 
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Stevenson, F. S., Robert Grosseteste, 1899. Vol. 70, No. 1816. 

Thilly, F., Introduction to Ethics, 1900. Vol. 70, No. 1825. 

Wallace, A. R., Studies, Scientific and Social, 1900. Vol. 72, No. 1854. 

Sime, J., William Herschel and His Work, 1900. Vol. 72, No. 1856. 

Rand, B. (Editor), The Life, Unpublished Letters, and Philosophical Regi¬ 
men of Anthony, Earl of Shaftesbury, 1900; and Robertson, J. M. 
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Bacon, Rev. J. M., By Land and Sea, 1901. Vol. 72, No. 1865. 

Jordan, W. L., Essays in Illustration of the Action of Astral Gravitation 
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Goblot, E., Le Vocabulaire Philosophique, 1901. Vol. 72, No. 1877. 

Fraser, A. C. (Editor), The Works of George Berkeley, 1901. Vol. 73, 
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Frazer, P., Bibliotics, 1901. Vol. 73, No. 1883. 

Caldecott, A., The Philosophy of Religion in England and America, 1901. 
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Review of four physical books. Vol. 73, No. 1887. 

Maher, M., Psychology: Empirical and Rational, 1901. Vol. 73 , No. 
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Mezes, S. E., Ethics, 1901. Vol. 73, No. 1895. 

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Richardson, E. C., Classification, Theoretical and Practical, 1901. Vol. 74, 
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Vallery-Radot, R. (Translator: Mrs. R. L. Devonshire), The Life of 
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Giddings, F. H., Inductive Sociology, 1902. Vol. 74, No. 1918. 

Report on the Meeting of the National Academy of Sciences, Washington, 
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Emerson, E. R., The Story of the Vine, 1902. Vol. 74, No. 1926. 
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Review of four chemistry text-books, 1902. Vol. 75, No. 1934. 

Royce, J., The World and the Individual, Vol. II., 1901. Vol. 75, No. 
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Aikens, H. A., The Principles of Logic, 1902. Vol. 75, No. 1942. 

Drude, P., The Theory of Optics, 1902. Vol. 75, No. 1944. 

Valentine, E. S., Travels in Space, 1902; and Walker, F., Aerial Naviga¬ 
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Baillie, J. B., The Origin and Significance of Hegel’s Logic, 1901. Vol. 75, 
No. 1950. 

Forsyth, A. R., Theory of Differential Equations, Vol. IV., 1902. Vol. 75, 
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Ellwanger, G. V/., The Pleasures of the Table, 1902. Vol. 75, No. 1955. 
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Smith, Rev. T., Euclid: His Life and System, 1902. Vol. 76, No. 1961. 
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Hibben, J. G., Hegel’s Logic, 1902. Vol. 76, No. 1977. 

Mellor, J. W., Higher Mathematics for Students of Chemistry and Physics, 
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Sturt, H. C. (Editor), Personal Idealism, 1902. Vol. 76, No. 1979. 
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Clerke, Agnes M., Problems in Astrophysics, 1903. Vol. 77, No. 1987. 
Michelson, A. A., Light Waves and their Uses, 1903; and Fleming, J. A., 
Waves and Ripples in Water, 1902. Vol. 77, No. 1989. 


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3*7 

Note on Sir Norman Lockyer. Vol. 77, No. 1794. 

Note on British and American Science, 1903. Vol. 77, No. 1996. 

Welby, Lady Victoria, What is Meaning? 1903; and Russell B, The Prin¬ 
ciples of Mathematics, 1903. Vol. 77, No. 1998. 

Note on the Practical Application of the Theory of Functions, 1903. Vol. 
77, No. 1999. 

Fahie, J. J., Galileo. Vol. 78, No. 2015. 

Halsey, F. A., The Metric Fallacy, and Dale, S. S., The Metric Failure in 
the Textile Industry. Vol. 78, No. 2020. 

Newcomb, S., The Reminiscences of an Astronomer, 1903. Vol. 78, No. 
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Boole, Mrs. M. E., Lectures on the Logic of Arithmetic, 1903; and Bowden, 
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Levy-Bruhl, L. (Translator: Kathleen de Beaumont-Klein), The Philoso¬ 
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Turner, W., History of Philosophy, 1903. Vol. 79, No. 2036. 

Duff, R. A., Spinoza’s Political and Ethical Philosophy. Vol. 79, No. 
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Allbutt, T. C., Notes on the Composition of Scientific Papers, 1904. Vol. 

79, No. 2039. 

Sylvester, J. J., The Collected Mathematical Papers of, Vol. I. Vol. 79, 
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Renouvier, Ch., Les Demiers Entretiens, 1904, and Dewey, J., Studies in 
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Royce, J., Outlines of Psychology. Vol. 79, No. 2048. 

Straton, G. M., Experimental Psychology and its Bearing upon Culture. 
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Boole, Mrs. M. E., The Preparation of the Child for Science, 1904. Vol. 

80, No. 2062. 

Royce, J., Herbert Spencer, 1904. Vol. 80, No. 2065. 

Strutt, R. J., The Becquerel Rays and the Properties of Radium, 1904. 
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Flint, R., Philosophy as Scientia Scientiarum, 1904; and Peirce, C. S., A 
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Carnegie, A., James Watt, 1905. Vol. 80, No. 2087. 

Ross, E. A., Foundations of Sociology, 1905, and Sociological Papers, 1905, 
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Varigny, H. de, La Nature et la Vie, 1905. Vol. 81, No. 2101. 

Note on Mr. G. W. Hill’s Moon Theory. Vol. 81, 2103. 

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Gosse, E., Sir Thomas Browne, 1905. Vol. 81, No. 2111. 

Rutherford, E., Radio-Activity, 1905. Vol. 82, No. 2116. 

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